T(11,2) - Revision history

ScottKnotPageRobot at 15:38, 31 August 2005

2005-08-31T15:38:12Z

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-<!-- This page was  generated from the splice template "Torus_Knot_Splice_Template". Please do not edit! -->
+<!-- This page was generated from the splice template [[Torus_Knot_Splice_Base]]. Please do not edit!
 {{Torus Knot Page|
 m = 11 |

ScottKnotPageRobot at 16:16, 30 August 2005

2005-08-30T16:16:00Z

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ScottTestRobot at 00:45, 29 August 2005

2005-08-29T00:45:58Z

← Older revision		Revision as of 20:45, 28 August 2005
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			<!-- This knot page was produced from [[Torus Knots Splice Template]] -->

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		⚫	{{Torus Knot Page Header\|m=11\|n=2\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-8,9,-10,11,-1,2,-3,4,-5,6,-7,8,-9,10,-11,1,-2,3,-4,5,-6,7/goTop.html}}
	{\| align=left
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⚫	\|{{Torus Knot ~~Site~~ ~~Links~~\|m=11\|n=2\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-8,9,-10,11,-1,2,-3,4,-5,6,-7,8,-9,10,-11,1,-2,3,-4,5,-6,7/goTop.html}}

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	{{Vassiliev Invariants}}		{{Vassiliev Invariants}}

	~~===[[~~Khovanov Homology~~]]=~~==		{{Khovanov Homology\|table=<table border=1>

	The coefficients of the monomials <math>t^rq^j</math> are shown, along with their alternating sums <math>\chi</math> (fixed <math>j</math>, alternation over <math>r</math>). The squares with <font class=HLYellow>yellow</font> highlighting are those on the "critical diagonals", where <math>j-2r=s+1</math> or <math>j-2r=s+1</math>, where <math>s=</math>{{Data:{{PAGENAME}}/Signature}} is the signature of {{PAGENAME}}. Nonzero entries off the critical diagonals (if any exist) are highlighted in <font class=HLRed>red</font>.

	<center><table border=1>
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	<td width=12.5%><table cellpadding=0 cellspacing=0>		<td width=12.5%><table cellpadding=0 cellspacing=0>
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	<tr align=center><td>11</td><td bgcolor=yellow>1</td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>		<tr align=center><td>11</td><td bgcolor=yellow>1</td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
	<tr align=center><td>9</td><td bgcolor=yellow>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>		<tr align=center><td>9</td><td bgcolor=yellow>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
	</table>~~</center>~~		</table>}}

	{{Computer Talk Header}}		{{Computer Talk Header}}
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	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[2, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}]</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[2, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}]</nowiki></pre></td></tr>
	<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>alex = Alexander[TorusKnot[11, 2]][t]</nowiki></pre></td></tr>		<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>alex = Alexander[TorusKnot[11, 2]][t]</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -5 -4 -3 -2 1 2 3 4 5		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -5 -4 -3 -2
	-1 + t - t + t - t + ~~- + t - t + t - t + t~~		-1 + Alternating - Alternating + Alternating - Alternating +

	~~t</nowiki></pre></td></tr>~~		1 2 3
			----------- + Alternating - Alternating + Alternating -
			Alternating

			4 5
			Alternating + Alternating</nowiki></pre></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>Conway[TorusKnot[11, 2]][z]</nowiki></pre></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>Conway[TorusKnot[11, 2]][z]</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 4 6 8 10		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 4 6 8 10
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	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{0, 55}</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{0, 55}</nowiki></pre></td></tr>
	<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>Kh[TorusKnot[11, 2]][q, t]</nowiki></pre></td></tr>		<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>Kh[TorusKnot[11, 2]][q, t]</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 9 11 13 2 17 3 17 4 21 5 21 6 25 7		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 9 11 2 13 3 17 4 17
	q + q + q ~~t +~~ q t + q ~~t +~~ q t + q ~~t +~~ q t +		q + q + Alternating q + Alternating q + Alternating q +

			5 21 6 21 7 25
			Alternating q + Alternating q + Alternating q +

			8 25 9 29 10 29
			Alternating q + Alternating q + Alternating q +

	25 8 29 ~~9 29 10~~ 33 11		11 33
	q ~~t +~~ q ~~t + q t + q t~~</nowiki></pre></td></tr>		Alternating q</nowiki></pre></td></tr>
	</table>		</table>

	{{Category:Knot Page}}		[[Category:Knot Page]]

ScottTestRobot at 23:43, 28 August 2005

2005-08-28T23:43:26Z

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-|Visit [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-8,9,-10,11,-1,2,-3,4,-5,6,-7,8,-9,10,-11,1,-2,3,-4,5,-6,7/goTop.html {{PAGENAME}}'s page] at [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/html/start.html Knotilus]!
+|{{Torus Knot Site Links|m=11|n=2|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-8,9,-10,11,-1,2,-3,4,-5,6,-7,8,-9,10,-11,1,-2,3,-4,5,-6,7/goTop.html}}
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 {{Polynomial Invariants}}
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   q   t  + q   t  + q   t   + q   t</nowiki></pre></td></tr>
 </table>

ScottTestRobot at 01:24, 28 August 2005

2005-08-28T01:24:20Z

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DrorsRobot at 02:46, 27 August 2005

2005-08-27T02:46:01Z

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DrorsRobot at 23:35, 26 August 2005

2005-08-26T23:35:22Z

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DrorsRobot at 23:33, 26 August 2005

2005-08-26T23:33:16Z

← Older revision		Revision as of 19:33, 26 August 2005
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	<!-- d $Failedmath . uwo . c$Failedv$ileddge] at [h$Failedn.matuwo . ca		<!-- $Failed $Failedn$F $Failedmath . uwo . c$Failedv$ileddge] at [h$Failedn.matuwo . ca
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	c$Faidml K$FaidaFailedsKt$iledpa$Faidtoront$iledailedt pres$Failedgrams\|Planar dir entatio$Failede="padding-left: 1em;" \| X<sub>3146<u b 152/s$Failed62</sub>		c$Faidml K$FaidaFailedsKt$iledpa$Faidtoront$iledailedt pres$Failedgrams\|Planar dir entatio$Failede="padding-left: 1em;" \| X<sub>3146<u b 152/s$Failed62</sub>

DrorsRobot at 23:28, 26 August 2005

2005-08-26T23:28:38Z

New page

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|'''[[GausCeGss cod$Failede=$Faile$Failed1, 2, -3, 1}
'$Failed (Dowk-Thistlewaite) Codes|Dowker-Thistl$Failedepa$Faedial Invariants|name=T(3,2)}}

===[[Finite Type (Vassiliev)nvaanFailed===$Failed'''
|style="padding-left: 1em;"$Failed)
|}

[[KhovHomolo$Failedeffi oven$Failed> are shoFaile</math>, over ternation < math</math>). The squares with <f$FailedYe2</math>, where <math>s=</math>2 is the signHLRed$Faile
<center><table border=1>
<tr align=center>
<td wid$Failedled$Failed>j</td><td> </td$Failed/tr>
</table></td>
<td wi$Failed/td ><td width=12.5%>1</td ><td width=12.5%>2</$Failedlednter><td>9</td><td> </td><td>&nbsp$Failedtd bgcolor=yellow>1</$Faileded<td> </td><t$Failedo$Failedo$Fail$Failediled>$Failed&$Failedd$Failed>$Failed>$Fa$Failed style="color: red; borpadding:0"><< KnotTheory$Failed
</tr>$Failed="border: 0px; pa$Failedy$Failed9$Failedd$Failed<$Failed;$Failed=$Failed $Failedn$Failedi$Failedn$Failedp $Failedd$Faile$Failed
ailed > -----$Failed------
tdtd><pre style="color: red; border: 0px; padding: 0em"><nowiki>PD[TorusKnot[3, 2]]</now$Failededp$Failed $Failedo$F$Failedd,$Faileds$Failedi$Failed<$Failedo$Failede$Failedk$Failedi$Failedp$Failedde[-2, 3, -1, 2, -3, 1]</nowiki></pre></td></$Failedolor: bl$Failedn[5]:=</nowiki></$Failedrd$Failedo$Failed>$Failedea$Failed<$Failedd$Failed $Failedn0rpadding:0<$Failed3$Failedr$Failed: $Failed  </now$Failed=borde $Failed -1 - t/$Failed<$Failedo$Failed<$Failede$Failed $Failedd$Failed>$Failede$Failed $Failede$Failed 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><t$Failedadding: 0em"><now$Failed=$Failed/$Faileda$Failede$Failedm$Failed&$Failedr$Failed<$Failed>$Failed<$FailedK$Failedt$Failede$Failed $Failednowiki>Out[9]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{3, 2}</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>J=Jones[TorusKnot[3, 2]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[10]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 3 4
q + q - q</nowiki></pre></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>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[11]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[3, 1]}</nowiki></pre></td></tr>
Include[ColouredJonesM.mhtml]
<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>A2Invariant[TorusKnot[3, 2]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[12]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 4 6 8 12 14
q + q + 2 q + q - q - q</nowiki></pre></td></tr>
<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>Kauffman[TorusKnot[3, 2]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[13]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 2
-4 2 z z z z
-a - -- + -- + -- + -- + --
2 5 3 4 2
a a a a a</nowiki></pre></td></tr>
<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>{Vassiliev[2][TorusKnot[3, 2]], Vassiliev[3][TorusKnot[3, 2]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{0, 1}</nowiki></pre></td></tr>
<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>Kh[TorusKnot[3, 2]][q, t]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 3 5 2 9 3
q + q + q t + q t</nowiki></pre></td></tr>
</table>