T(7,3): Difference between revisions
From Knot Atlas
Jump to navigationJump to search
DrorsRobot (talk | contribs) No edit summary |
DrorsRobot (talk | contribs) No edit summary |
||
| Line 1: | Line 1: | ||
<!-- Script generated - do not edit! --> |
<!-- Script generated - do not edit! --> |
||
<!-- ailedmath . uwo . c$Failedv$ildg at [h$Failedn.matuwo . ca |
|||
<!-- --> |
|||
-------- |
|||
c$Faidml K$FaidaFaedsKiledpaaidtort$edailedts$Failedams$Faileding-l$Failed$Failed62</sub> |
|||
<span id="top"></span> |
|||
{{Knot Navigation Links|prev=T(13,2)|next=T(5,4)}} |
|||
Visit [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,3,4,-6,-7,9,10,-12,-13,1,2,-4,-5,7,8,-10,-11,13,14,-2,-3,5,6,-8,-9,11,12,-14/goTop.html T(7,3)'s page] at [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/html/start.html Knotilus]! |
|||
Visit [http://www.math.toronto.edu/~drorbn/KAtlas/TorusKnots/7.3.html T(7,3)'s page] at the original [http://www.math.toronto.edu/~drorbn/KAtlas/index.html Knot Atlas]! |
|||
{{Knot Presentations|name=7_5}} |
|||
===[[Three Dimensional Invariants|Three dimensional invariants]]=== |
|||
{| |
|||
| Symmetry type |
|||
| {{Data:7_5/Symmetry Type}} |
|||
|- |
|- |
||
|'''[[GausCeGss cod$Failede=$Faile$Failed1, 2, -3, 1} |
|||
| Unknotting number |
|||
'$Failed (Dowk-Thistlewaite) Codes|DowrhtFaileda$FaediaInvariants|name=T(3,2$Failed=$Failedinite $Failediev)nvaanFailed===$Failed''' |
|||
| {{Data:7_5/Unknotting Number}} |
|||
|style="padding-left: 1em;"$Failed) |
|||
|- |
|||
| 3-genus |
|||
| {{Data:7_5/3-Genus}} |
|||
|- |
|||
| Bridge index (super bridge index) |
|||
| {{Data:7_5/Bridge Index}} ({{Data:7_5/Super Bridge Index}}) |
|||
|- |
|||
| Nakanishi index |
|||
| {{Data:7_5/Nakanishi Index}} |
|||
|} |
|} |
||
{{Polynomial Invariants|name=7_5}} |
|||
[[KhovHomolo$Failedeffi oven$Failed> are shoFaile</math>, over ternation < math</math>). e sques with <f$FailedYe2</math>, where <math>s=</th > 2 the signHLRed$Failedrder=1> |
|||
{{Vassiliev Invariants|name=7_5}} |
|||
<tr align=center> |
|||
{{Khovanov Invariants|name=7_5}} |
|||
<td wid$Failedled$Fai$Failed$Failed/tr> |
|||
{{Quantum Invariants|name=7_5}} |
|||
</table></td> |
|||
<td wi$F$Failedtd>9</td><td> </td><td> $Failedtd bgcolor=yellow>1</$Fl$Faileddd$Failed>$Failed>$Fa$Failed style="color: red; borpadding:0">&$FailedTheory$Failed |
|||
</tr>$Failed="border: 0$Failed$Failed;$Failed=$Failed $Failedn$Failedi$Failedn$Failedp $Failedd$Faile$Failed |
|||
ailed > -----$Failed------ |
|||
td$Failed; padding: 0em"><nowiki>PD[TorusKnot[3, 2]]</now$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$$Failed/$Failedrd$Failedo$Faed > $Failea$Failed<$Failedd$Failed $Failedn0rpadding:0<$Failed3$Failedr$Failed: $Failed </now$Failed=borde $Failed - t |
|||
-($Failediled < $Fai |
|||
$Failed$Failedailedd$Failed>$Failede$Failed $Failede$Failed 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><t$Failedadding: 0$Failedlede$Failedm$Failed&$Failedr$Failed<$Failed>$Failed<$FailedK$Failedt$Failede$Failed $Failednowiki>Out[9]= </nowiki></pre></td><td><pre style="color: $Failedi>{3, 2}</nowiki>$Failedo$Failedrpaddin $Failed/$Failed:$Failede$Failedt$Failedd$Failed>$Failedd$Failedt$Failedcpadding0$Failed"8ding: 0em"><nowiki>Select[AllK$Failed1/q) === Jones[#]$Failedr$Failedp$Failed:$Failedo$Failed>$Failedl$Failedn$Failedl$Failede$Failede$Failedr$Failedd$Failedl$Failed1$Failedi></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></math> |
|||
Revision as of 18:28, 26 August 2005
