T(5,4) - Revision history

ScottKnotPageRobot at 15:38, 31 August 2005

2005-08-31T15:38:07Z

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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 = 5 |

ScottKnotPageRobot at 16:15, 30 August 2005

2005-08-30T16:15:53Z

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ScottTestRobot at 00:45, 29 August 2005

2005-08-29T00:45:50Z

← 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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	<span id="top"></span>		<span id="top"></span>
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	{{Knot Navigation Links\|ext=jpg}}		{{Knot Navigation Links\|ext=jpg}}

		⚫	{{Torus Knot Page Header\|m=5\|n=4\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/14,15,-3,-5,-7,10,11,12,-15,-2,-4,7,8,9,-12,-14,-1,4,5,6,-9,-11,-13,1,2,3,-6,-8,-10,13/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.jpg]]
⚫	\|{{Torus Knot ~~Site~~ ~~Links~~\|m=5\|n=4\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/14,15,-3,-5,-7,10,11,12,-15,-2,-4,7,8,9,-12,-14,-1,4,5,6,-9,-11,-13,1,2,3,-6,-8,-10,13/goTop.html}}

	{{:{{PAGENAME}} Quick Notes}}
	\|}

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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>
	<tr align=center>		<tr align=center>
	<td width=14.2857%><table cellpadding=0 cellspacing=0>		<td width=14.2857%><table cellpadding=0 cellspacing=0>
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	<tr align=center><td>13</td><td bgcolor=red>1</td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>		<tr align=center><td>13</td><td bgcolor=red>1</td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow> </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=red>1</td><td bgcolor=yellow> </td><td bgcolor=yellow> </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=red>1</td><td bgcolor=yellow> </td><td bgcolor=yellow> </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[4, {1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3}]</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[4, {1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3}]</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[5, 4]][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[5, 4]][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> -6 -5 -2 2 5 6		<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> -6 -5 -2 2
	-1 + t - t + t + t - ~~t + t</nowiki></pre></td></tr>~~		-1 + Alternating - Alternating + Alternating + Alternating -

			5 6
			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[5, 4]][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[5, 4]][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 12		<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 12
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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, 50}</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, 50}</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[5, 4]][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[5, 4]][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> 11 13 15 2 19 3 17 4 19 4 21 5 23 5		<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> 11 13 2 15 4 17 3 19
	q + q + q ~~t +~~ q t + q ~~t +~~ q t + q ~~t +~~ q t +		q + q + Alternating q + Alternating q + Alternating q +

			4 19 6 19 5 21
			Alternating q + Alternating q + Alternating q +

			6 21 5 23 7 23
			Alternating q + Alternating q + Alternating q +

	19 6 21 6 23 7 25 7 23 8 27 9		8 23 7 25 9 27
	q ~~t +~~ q t + q ~~t +~~ q t + q ~~t +~~ q t</nowiki></pre></td></tr>		Alternating q + Alternating q + Alternating q</nowiki></pre></td></tr>
	</table>		</table>

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

ScottTestRobot at 23:43, 28 August 2005

2005-08-28T23:43:16Z

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 |- valign=top
 |[[Image:{{PAGENAME}}.jpg]]
-|Visit [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/14,15,-3,-5,-7,10,11,12,-15,-2,-4,7,8,9,-12,-14,-1,4,5,6,-9,-11,-13,1,2,3,-6,-8,-10,13/goTop.html {{PAGENAME}}'s page] at [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/html/start.html Knotilus]!
+|{{Torus Knot Site Links|m=5|n=4|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/14,15,-3,-5,-7,10,11,12,-15,-2,-4,7,8,9,-12,-14,-1,4,5,6,-9,-11,-13,1,2,3,-6,-8,-10,13/goTop.html}}
 {{:{{PAGENAME}} Quick Notes}}
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 {{Knot Presentations}}
 {{Polynomial Invariants}}
 {{Vassiliev Invariants}}
@@ Line 149: / Line 133: @@
   q   t  + q   t  + q   t  + q   t  + q   t  + q   t</nowiki></pre></td></tr>
 </table>

ScottTestRobot at 01:24, 28 August 2005

2005-08-28T01:24:27Z

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DrorsRobot at 02:46, 27 August 2005

2005-08-27T02:46:09Z

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DrorsRobot at 23:35, 26 August 2005

2005-08-26T23:35:31Z

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DrorsRobot at 23:33, 26 August 2005

2005-08-26T23:33:21Z

← Older revision		Revision as of 19:33, 26 August 2005
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	<!-- ~~a ledmath . uwo . c~~$~~Failedv$ildg[h$Failedn~~.matuwo . ca		<!-- $Faileddn.matuwo . ca
	--------		--------
	c$~~Faidml K~~$~~FaidaFaedsKiledaidtort~~$~~edaidts~~$~~Faileds$Failedg-l~~$Failed$~~Fail~~$~~Failedd~~$Failede=$Faile$Failed1, 2, -3, 1}		caidmK$Faidaileds$idpa$Faidnt$ileddtres$Failed$Failedadd$Failedm;" \| X<sub>314$Failed''[[GausCeGss cod$Failede=$Faile$Failed1, 2, -3, 1}
			'$Failed (Dowk-ThistlaeCes\|Dowr - T2aepa$Faeal Invarnts\|name=T(3,2)}}
	'$Failed (Dowk-Thistlewaite) Codes\|DowrhtFaileda$FaediaInvariants\|name=T(3,2$Failed=$Failedinite $Failediev)nvaanFl=$iled''$Faileddding-left: 1em;"$Failed)

			===[[Finite Type (Vassilievvnid===$F$Failedyle="padding-left: 1em;"$Failed)
	\|}		\|}

	[[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~~>		[[KhovHomolo$Failedeffi oven$Failed> are shoFaile</math>, over ternationmathmath>). The squares th < failedYe2</math>, where <math>s=</math>22 signHLRed$Fail the<center><$ilednenter>
		⚫	<td wid$Failedled$Failed>j</td><td> </td$Failed/tr>
	<tr cter>
			</ta Failed
⚫	<td wid$Failedled~~$Fai~~$Failed$Failed/tr>
			-------------
	</table></td>
		⚫	$Failedlednte<td>9</td>$Failed><t$Failedo$Failedo$Fail$Failediled>$Failed&$Failedd$Failed>$Faed > $Fa$Fled style="colo$Failededd$Failed<$Failed;$Failed=$Failed $Failedn$Failedi$Failedn$Faidp $Faidd$Faile$Failailed > --(--(-$Failed------)) tdtd><pre style="color: red; border: 0px; padding: 0em"><nowiki>PD[TorusKnot[3, 2]]</now$Failededp$Failed $Failedo$F$F$Failedo$Failede$Failedk$Failedi$Failedp$Failedde[-2, 3, -1, 2, -3, 1]</nowiki></pre></td><Failedolor:bl$Faidn[5]:=</nowiki></$Faedrd$Faido$Failed>$Failedea$Failed<$Failedd$Failed $Failedn0rpadding:0<$Failed3$Failedr$Failednbsp ((($Failed & ) nbsp; ) & )/now$Faile t
	<td wi$F$$Failed;</td><td>&nbsp$Failedtd bgcolor=yellow>1</$Fl$Faileddd$Failed>$Failed>$Fa$Failed style="color: red; borpding:0d;$Failed=$Failed $Failedn$Failedi$Failedn$Failedp $Failedd$Fae$Failediled > -----$Failed------
			-$Failed+ borde $Failed < $Fa
⚫	~~td$Failed~~; padding: 0em"><nowiki>PD[TorusKnot[3, 2]]</now$Failededp$Failed $Failedo$F$~~Failedd,$Faileds$Failedi$Failed<~~$Failedo$~~ilede~~$Failedk$Failedi$Failedp$~~Failde~~[-2, 3, -1, 2, -3, 1]</nowiki></pre></td></$Failedolor: bl$~~$Failed~~/$~~Failedrd~~$~~Failedo~~$~~Faed~~ > $~~Failea~~$Failed<$Failedd$Failed $Failedn0rpadding:0<$Failed3$Failedr$~~Failed:~~ $Failed &~~nbsp;<~~/now$~~Failed=borde~~ ~~$Failed~~ - t
			$Failededo$Failed<$Failede$Failed $Failedd$Failed>$Failede$Failed $Failede$Failepadd$Failedpr</td><t$Failedadding:$Failedailed=$Failed/$Faileda$Failede$Failedm$Failed&$Failedr$Failed<$Failed>$Failed<$FailedK$Failedt$Failede$Failed $Failedn$Failediki></pre></td><td><p$Failedding: 0em"><nowik$Failed/$Failed>$Failedepadding:0<$Failed<$Failed:$Failedi$Failed"pai$Failed;$Failedi$Failed>$Fapaddg: 0em"><nowiki>S$Faileds$Failedq$Failed<$Failedl$Failedr$Failedk$Failedl$Failedi$Failedt$Failedp$Failedt$Failedi$FailedK$Failedt$Failedorder: 0px; padding: 0em"><nowiki>Out[12]= &nb$Failedyle="color: blackpadding:0<wiki > 8 2 + 2 q $Failedi$Failedr$Failed $Failedpcolor: red; border: 0px; padding: 0emn$Failed]$Failedd$Failedd$Failedd$Failed 3
	-($Failediled < $Fai
		⚫	-8 z-$Failed
	$Failed$Failedailedd$Failed>$Failede$Failed $Failede$Failed 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><t$Failedadding: 0$Faedlede$Failedm$Faid&$Failedr$Failed<$Faed > $Fail<$FailedK$Failedt$Failede$Failed $Failednowiki>Out[9]=   </nowiki></pre></td><td><pre style="color: $Fa$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; paddin$Failed2 14
			2 5 3 4 2
	q + q +$Failed<$Failedl$Failed:d$Failedr$Failed $Failed,$Failed>$Failedo$Failedl$Failed -8 z $Failed- 2
			a a a a a</nowiki></pre></td></tr>
⚫	a $Failed~~></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>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>Out[14]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{0, 1}</nowiki></pre></td></tr>
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	<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		<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>		q + q + q t + q t</nowiki></pre></td></tr>
	</table~~></math~~>		</table>

DrorsRobot at 23:28, 26 August 2005

2005-08-26T23:28:43Z

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DrorsRobot at 21:28, 26 August 2005

2005-08-26T21:28:31Z

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