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{{Hoste-Thistlethwaite Knot Page|
{{Hoste-Thistlethwaite Knot Page|
n = 11 |
n = 11 |
t = a |
t = <nowiki>a</nowiki> |
k = 147 |
k = 147 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-5,2,-1,3,-10,4,-8,5,-2,6,-9,7,-11,8,-3,9,-7,10,-4,11,-6/goTop.html |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-5,2,-1,3,-10,4,-8,5,-2,6,-9,7,-11,8,-3,9,-7,10,-4,11,-6/goTop.html |
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<td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td>
<td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td>
</tr>
</tr>
<tr valign=top><td colspan=2>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</td></tr>
<tr valign=top><td colspan=2><nowiki>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</nowiki></td></tr>
</table>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Crossings[Knot[11, Alternating, 147]]</nowiki></pre></td></tr>
<table><tr align=left>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>11</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[3]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>PD[Knot[11, Alternating, 147]]</nowiki></pre></td></tr>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[2]:=</code></td>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[3]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[4, 2, 5, 1], X[10, 4, 11, 3], X[16, 6, 17, 5], X[20, 8, 21, 7],
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Crossings[Knot[11, Alternating, 147]]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[2]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>11</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[3]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[Knot[11, Alternating, 147]]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[3]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[X[4, 2, 5, 1], X[10, 4, 11, 3], X[16, 6, 17, 5], X[20, 8, 21, 7],
X[2, 10, 3, 9], X[22, 11, 1, 12], X[18, 13, 19, 14], X[8, 16, 9, 15],
X[2, 10, 3, 9], X[22, 11, 1, 12], X[18, 13, 19, 14], X[8, 16, 9, 15],
X[12, 17, 13, 18], X[6, 20, 7, 19], X[14, 21, 15, 22]]</nowiki></pre></td></tr>
X[12, 17, 13, 18], X[6, 20, 7, 19], X[14, 21, 15, 22]]</nowiki></code></td></tr>
</table>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[4]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>GaussCode[Knot[11, Alternating, 147]]</nowiki></pre></td></tr>
<table><tr align=left>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[4]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>GaussCode[1, -5, 2, -1, 3, -10, 4, -8, 5, -2, 6, -9, 7, -11, 8, -3, 9,
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[4]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[Knot[11, Alternating, 147]]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[4]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[1, -5, 2, -1, 3, -10, 4, -8, 5, -2, 6, -9, 7, -11, 8, -3, 9,
-7, 10, -4, 11, -6]</nowiki></pre></td></tr>
-7, 10, -4, 11, -6]</nowiki></code></td></tr>
</table>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[5]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>BR[Knot[11, Alternating, 147]]</nowiki></pre></td></tr>
<table><tr align=left>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[Knot[11, Alternating, 147]]</nowiki></pre></td></tr>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[5]:=</code></td>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[6]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Show[DrawMorseLink[Knot[11, Alternating, 147]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:K11a147_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[6]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[7]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>alex = Alexander[Knot[11, Alternating, 147]][t]</nowiki></pre></td></tr>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BR[Knot[11, Alternating, 147]]</nowiki></code></td></tr>
<tr align=left>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -4 6 17 32 2 3 4
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[5]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BR[Knot[11, Alternating, 147]]</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[6]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Show[DrawMorseLink[Knot[11, Alternating, 147]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:K11a147_ML.gif]]</td></tr><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[6]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>-Graphics-</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[7]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>alex = Alexander[Knot[11, Alternating, 147]][t]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[7]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -4 6 17 32 2 3 4
-39 - t + -- - -- + -- + 32 t - 17 t + 6 t - t
-39 - t + -- - -- + -- + 32 t - 17 t + 6 t - t
3 2 t
3 2 t
t t</nowiki></pre></td></tr>
t t</nowiki></code></td></tr>
</table>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Conway[Knot[11, Alternating, 147]][z]</nowiki></pre></td></tr>
<table><tr align=left>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[8]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 4 6 8
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td>
1 + 2 z - z - 2 z - z</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[9]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></pre></td></tr>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Conway[Knot[11, Alternating, 147]][z]</nowiki></code></td></tr>
<tr align=left>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[11, Alternating, 147]}</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[10]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{KnotDet[Knot[11, Alternating, 147]], KnotSignature[Knot[11, Alternating, 147]]}</nowiki></pre></td></tr>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[8]:=</code></td>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[10]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{151, 2}</nowiki></pre></td></tr>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 4 6 8
1 + 2 z - z - 2 z - z</nowiki></code></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[11]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>J=Jones[Knot[11, Alternating, 147]][q]</nowiki></pre></td></tr>
</table>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[11]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -3 4 9 2 3 4 5 6
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[9]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[9]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[11, Alternating, 147]}</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[10]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{KnotDet[Knot[11, Alternating, 147]], KnotSignature[Knot[11, Alternating, 147]]}</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[10]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{151, 2}</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[11]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>J=Jones[Knot[11, Alternating, 147]][q]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[11]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -3 4 9 2 3 4 5 6
-15 + q - -- + - + 21 q - 24 q + 25 q - 21 q + 16 q - 10 q +
-15 + q - -- + - + 21 q - 24 q + 25 q - 21 q + 16 q - 10 q +
2 q
2 q
Line 78: Line 138:
7 8
7 8
4 q - q</nowiki></pre></td></tr>
4 q - q</nowiki></code></td></tr>
</table>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[12]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></pre></td></tr>
<table><tr align=left>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[12]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[11, Alternating, 147], Knot[11, Alternating, 322]}</nowiki></pre></td></tr>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[12]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[12]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[11, Alternating, 147], Knot[11, Alternating, 322]}</nowiki></code></td></tr>
</table>
<table><tr align=left>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[13]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>A2Invariant[Knot[11, Alternating, 147]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[13]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -8 2 3 2 2 4 6 8 10 12
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[13]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>A2Invariant[Knot[11, Alternating, 147]][q]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[13]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -8 2 3 2 2 4 6 8 10 12
-1 + q - -- + -- - -- + 4 q - 5 q + 5 q - 2 q + 2 q + 3 q -
-1 + q - -- + -- - -- + 4 q - 5 q + 5 q - 2 q + 2 q + 3 q -
6 4 2
6 4 2
Line 89: Line 159:
14 16 18 20 22 24
14 16 18 20 22 24
3 q + 4 q - 3 q - q + q - q</nowiki></pre></td></tr>
3 q + 4 q - 3 q - q + q - q</nowiki></code></td></tr>
</table>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[14]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kauffman[Knot[11, Alternating, 147]][a, z]</nowiki></pre></td></tr>
<table><tr align=left>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 2
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[14]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kauffman[Knot[11, Alternating, 147]][a, z]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[14]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 2
2 4 2 4 z 7 z 5 z 3 z 2 z 5 z
2 4 2 4 z 7 z 5 z 3 z 2 z 5 z
1 + -- + -- + -- - --- - --- - --- - --- - a z - 3 z + -- - ---- -
1 + -- + -- + -- - --- - --- - --- - --- - a z - 3 z + -- - ---- -
Line 125: Line 200:
----- + ---- + ----- + ---- + ----- + -----
----- + ---- + ----- + ---- + ----- + -----
2 5 3 a 4 2
2 5 3 a 4 2
a a a a a</nowiki></pre></td></tr>
a a a a a</nowiki></code></td></tr>
</table>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[15]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{Vassiliev[2][Knot[11, Alternating, 147]], Vassiliev[3][Knot[11, Alternating, 147]]}</nowiki></pre></td></tr>
<table><tr align=left>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{2, 4}</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[16]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kh[Knot[11, Alternating, 147]][q, t]</nowiki></pre></td></tr>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[15]:=</code></td>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[16]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 3 1 3 1 6 3 9 6 q
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Vassiliev[2][Knot[11, Alternating, 147]], Vassiliev[3][Knot[11, Alternating, 147]]}</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[15]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{2, 4}</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[16]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kh[Knot[11, Alternating, 147]][q, t]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[16]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 3 1 3 1 6 3 9 6 q
12 q + 10 q + ----- + ----- + ----- + ----- + ---- + --- + --- +
12 q + 10 q + ----- + ----- + ----- + ----- + ---- + --- + --- +
7 4 5 3 3 3 3 2 2 q t t
7 4 5 3 3 3 3 2 2 q t t
Line 138: Line 223:
9 4 11 4 11 5 13 5 13 6 15 6 17 7
9 4 11 4 11 5 13 5 13 6 15 6 17 7
7 q t + 9 q t + 3 q t + 7 q t + q t + 3 q t + q t</nowiki></pre></td></tr>
7 q t + 9 q t + 3 q t + 7 q t + q t + 3 q t + q t</nowiki></code></td></tr>
</table> }}
</table> }}

Revision as of 17:22, 1 September 2005

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K11a146

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K11a148

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See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

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Knot presentations

Planar diagram presentation X4251 X10,4,11,3 X16,6,17,5 X20,8,21,7 X2,10,3,9 X22,11,1,12 X18,13,19,14 X8,16,9,15 X12,17,13,18 X6,20,7,19 X14,21,15,22
Gauss code 1, -5, 2, -1, 3, -10, 4, -8, 5, -2, 6, -9, 7, -11, 8, -3, 9, -7, 10, -4, 11, -6
Dowker-Thistlethwaite code 4 10 16 20 2 22 18 8 12 6 14
A Braid Representative {{{braid_table}}}
A Morse Link Presentation K11a147 ML.gif

Three dimensional invariants

Symmetry type Chiral
Unknotting number
3-genus 4
Bridge index 3
Super bridge index Missing
Nakanishi index Missing
Maximal Thurston-Bennequin number Data:K11a147/ThurstonBennequinNumber
Hyperbolic Volume 17.2353
A-Polynomial See Data:K11a147/A-polynomial

[edit Notes for K11a147's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus Missing
Topological 4 genus Missing
Concordance genus
Rasmussen s-Invariant -2

[edit Notes for K11a147's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 151, 2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant
The G2 invariant

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

Same Jones Polynomial (up to mirroring, ): {K11a322,}

Vassiliev invariants

V2 and V3: (2, 4)
V2,1 through V6,9:
V2,1 V3,1 V4,1 V4,2 V4,3 V5,1 V5,2 V5,3 V5,4 V6,1 V6,2 V6,3 V6,4 V6,5 V6,6 V6,7 V6,8 V6,9

V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.

Khovanov Homology

The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ). The squares with yellow highlighting are those on the "critical diagonals", where or , where 2 is the signature of K11a147. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-4-3-2-101234567χ
17           1-1
15          3 3
13         71 -6
11        93  6
9       127   -5
7      139    4
5     1112     1
3    1013      -3
1   612       6
-1  39        -6
-3 16         5
-5 3          -3
-71           1
Integral Khovanov Homology

(db, data source)

  

Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session.

Modifying This Page

Read me first: Modifying Knot Pages.

See/edit the Hoste-Thistlethwaite Knot Page master template (intermediate).

See/edit the Hoste-Thistlethwaite_Splice_Base (expert).

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K11a146.gif

K11a146

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K11a148