Data:10 123/Integral Khovanov Homology: Difference between revisions

From Knot Atlas
Jump to navigationJump to search
No edit summary
 
No edit summary
 
(One intermediate revision by the same user not shown)
Line 1: Line 1:
{| border=1 cellspacing=0 cellpadding=1
{| border=1 cellspacing=0 cellpadding=1
|- align=center
|- align=center
|<math>\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}(10_123)</math>
|<math>\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}</math>
|<math>i=-1</math>
|<math>i=-1</math>
|<math>i=1</math>
|<math>i=1</math>
Line 10: Line 10:
|- align=center
|- align=center
|<math>r=-4</math>
|<math>r=-4</math>
|bgcolor=yellow|<math>{\mathbb Z}^4\oplus{\mathbb Z}_2</math>
|bgcolor=yellow|<math>{\mathbb Z}^{4}\oplus{\mathbb Z}_2</math>
|bgcolor=yellow|<math>{\mathbb Z}</math>
|bgcolor=yellow|<math>{\mathbb Z}</math>
|- align=center
|- align=center
|<math>r=-3</math>
|<math>r=-3</math>
|bgcolor=yellow|<math>{\mathbb Z}^6\oplus{\mathbb Z}_2^4</math>
|bgcolor=yellow|<math>{\mathbb Z}^{6}\oplus{\mathbb Z}_2^{4}</math>
|bgcolor=yellow|<math>{\mathbb Z}^4</math>
|bgcolor=yellow|<math>{\mathbb Z}^{4}</math>
|- align=center
|- align=center
|<math>r=-2</math>
|<math>r=-2</math>
|bgcolor=yellow|<math>{\mathbb Z}^9\oplus{\mathbb Z}_2^6</math>
|bgcolor=yellow|<math>{\mathbb Z}^{9}\oplus{\mathbb Z}_2^{6}</math>
|bgcolor=yellow|<math>{\mathbb Z}^6</math>
|bgcolor=yellow|<math>{\mathbb Z}^{6}</math>
|- align=center
|- align=center
|<math>r=-1</math>
|<math>r=-1</math>
|bgcolor=yellow|<math>{\mathbb Z}^10\oplus{\mathbb Z}_2^9</math>
|bgcolor=yellow|<math>{\mathbb Z}^{10}\oplus{\mathbb Z}_2^{9}</math>
|bgcolor=yellow|<math>{\mathbb Z}^9</math>
|bgcolor=yellow|<math>{\mathbb Z}^{9}</math>
|- align=center
|- align=center
|<math>r=0</math>
|<math>r=0</math>
|bgcolor=yellow|<math>{\mathbb Z}^11\oplus{\mathbb Z}_2^10</math>
|bgcolor=yellow|<math>{\mathbb Z}^{11}\oplus{\mathbb Z}_2^{10}</math>
|bgcolor=yellow|<math>{\mathbb Z}^11</math>
|bgcolor=yellow|<math>{\mathbb Z}^{11}</math>
|- align=center
|- align=center
|<math>r=1</math>
|<math>r=1</math>
|bgcolor=yellow|<math>{\mathbb Z}^9\oplus{\mathbb Z}_2^10</math>
|bgcolor=yellow|<math>{\mathbb Z}^{9}\oplus{\mathbb Z}_2^{10}</math>
|bgcolor=yellow|<math>{\mathbb Z}^10</math>
|bgcolor=yellow|<math>{\mathbb Z}^{10}</math>
|- align=center
|- align=center
|<math>r=2</math>
|<math>r=2</math>
|bgcolor=yellow|<math>{\mathbb Z}^6\oplus{\mathbb Z}_2^9</math>
|bgcolor=yellow|<math>{\mathbb Z}^{6}\oplus{\mathbb Z}_2^{9}</math>
|bgcolor=yellow|<math>{\mathbb Z}^9</math>
|bgcolor=yellow|<math>{\mathbb Z}^{9}</math>
|- align=center
|- align=center
|<math>r=3</math>
|<math>r=3</math>
|bgcolor=yellow|<math>{\mathbb Z}^4\oplus{\mathbb Z}_2^6</math>
|bgcolor=yellow|<math>{\mathbb Z}^{4}\oplus{\mathbb Z}_2^{6}</math>
|bgcolor=yellow|<math>{\mathbb Z}^6</math>
|bgcolor=yellow|<math>{\mathbb Z}^{6}</math>
|- align=center
|- align=center
|<math>r=4</math>
|<math>r=4</math>
|bgcolor=yellow|<math>{\mathbb Z}\oplus{\mathbb Z}_2^4</math>
|bgcolor=yellow|<math>{\mathbb Z}\oplus{\mathbb Z}_2^{4}</math>
|bgcolor=yellow|<math>{\mathbb Z}^4</math>
|bgcolor=yellow|<math>{\mathbb Z}^{4}</math>
|- align=center
|- align=center
|<math>r=5</math>
|<math>r=5</math>

Latest revision as of 08:06, 27 June 2006

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=-5} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=-3}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=-2} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{9}\oplus{\mathbb Z}_2^{6}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=0} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{11}\oplus{\mathbb Z}_2^{10}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=2} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{6}\oplus{\mathbb Z}_2^{9}} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{9}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{4}\oplus{\mathbb Z}_2^{6}}
Retrieved from "https://katlas.org/index.php?title=Data:10_123/Integral_Khovanov_Homology&oldid=1105320"