Data:K11a43/Integral Khovanov Homology: Difference between revisions
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{| border=1 cellspacing=0 cellpadding=1 |
{| border=1 cellspacing=0 cellpadding=1 |
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|- align=center |
|- align=center |
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|<math>\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} |
|<math>\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}</math> |
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|<math>i=5</math> |
|<math>i=5</math> |
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|<math>i=7</math> |
|<math>i=7</math> |
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|- align=center |
|- align=center |
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|<math>r=1</math> |
|<math>r=1</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^3</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{3}</math> |
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|bgcolor=yellow| |
|bgcolor=yellow| |
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|- align=center |
|- align=center |
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|<math>r=2</math> |
|<math>r=2</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^6\oplus{\mathbb Z}_2^3</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{6}\oplus{\mathbb Z}_2^{3}</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^3</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{3}</math> |
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|- align=center |
|- align=center |
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|<math>r=3</math> |
|<math>r=3</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^7\oplus{\mathbb Z}_2^6</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{7}\oplus{\mathbb Z}_2^{6}</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^6</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{6}</math> |
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|- align=center |
|- align=center |
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|<math>r=4</math> |
|<math>r=4</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^12\oplus{\mathbb Z}_2^7</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{12}\oplus{\mathbb Z}_2^{7}</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^7</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{7}</math> |
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|- align=center |
|- align=center |
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|<math>r=5</math> |
|<math>r=5</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^10\oplus{\mathbb Z}_2^12</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{10}\oplus{\mathbb Z}_2^{12}</math> |
||
|bgcolor=yellow|<math>{\mathbb Z}^12</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{12}</math> |
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|- align=center |
|- align=center |
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|<math>r=6</math> |
|<math>r=6</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}^10</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{10}</math> |
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|- align=center |
|- align=center |
||
|<math>r=7</math> |
|<math>r=7</math> |
||
|bgcolor=yellow|<math>{\mathbb Z}^9\oplus{\mathbb Z}_2^11</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{9}\oplus{\mathbb Z}_2^{11}</math> |
||
|bgcolor=yellow|<math>{\mathbb Z}^11</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{11}</math> |
||
|- align=center |
|- align=center |
||
|<math>r=8</math> |
|<math>r=8</math> |
||
|bgcolor=yellow|<math>{\mathbb Z}^5\oplus{\mathbb Z}_2^9</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{5}\oplus{\mathbb Z}_2^{9}</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^9</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{9}</math> |
||
|- align=center |
|- align=center |
||
|<math>r=9</math> |
|<math>r=9</math> |
||
|bgcolor=yellow|<math>{\mathbb Z}^3\oplus{\mathbb Z}_2^5</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{3}\oplus{\mathbb Z}_2^{5}</math> |
||
|bgcolor=yellow|<math>{\mathbb Z}^5</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{5}</math> |
||
|- align=center |
|- align=center |
||
|<math>r=10</math> |
|<math>r=10</math> |
||
|bgcolor=yellow|<math>{\mathbb Z}\oplus{\mathbb Z}_2^3</math> |
|bgcolor=yellow|<math>{\mathbb Z}\oplus{\mathbb Z}_2^{3}</math> |
||
|bgcolor=yellow|<math>{\mathbb Z}^3</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{3}</math> |
||
|- align=center |
|- align=center |
||
|<math>r=11</math> |
|<math>r=11</math> |
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Latest revision as of 08:09, 27 June 2006
| [math]\displaystyle{ \dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} }[/math] | [math]\displaystyle{ i=5 }[/math] | [math]\displaystyle{ i=7 }[/math] |
| [math]\displaystyle{ r=0 }[/math] | [math]\displaystyle{ {\mathbb Z} }[/math] | [math]\displaystyle{ {\mathbb Z} }[/math] |
| [math]\displaystyle{ r=1 }[/math] | [math]\displaystyle{ {\mathbb Z}^{3} }[/math] | |
| [math]\displaystyle{ r=2 }[/math] | [math]\displaystyle{ {\mathbb Z}^{6}\oplus{\mathbb Z}_2^{3} }[/math] | [math]\displaystyle{ {\mathbb Z}^{3} }[/math] |
| [math]\displaystyle{ r=3 }[/math] | [math]\displaystyle{ {\mathbb Z}^{7}\oplus{\mathbb Z}_2^{6} }[/math] | [math]\displaystyle{ {\mathbb Z}^{6} }[/math] |
| [math]\displaystyle{ r=4 }[/math] | [math]\displaystyle{ {\mathbb Z}^{12}\oplus{\mathbb Z}_2^{7} }[/math] | [math]\displaystyle{ {\mathbb Z}^{7} }[/math] |
| [math]\displaystyle{ r=5 }[/math] | [math]\displaystyle{ {\mathbb Z}^{10}\oplus{\mathbb Z}_2^{12} }[/math] | [math]\displaystyle{ {\mathbb Z}^{12} }[/math] |
| [math]\displaystyle{ r=6 }[/math] | [math]\displaystyle{ {\mathbb Z}^{11}\oplus{\mathbb Z}_2^{10} }[/math] | [math]\displaystyle{ {\mathbb Z}^{10} }[/math] |
| [math]\displaystyle{ r=7 }[/math] | [math]\displaystyle{ {\mathbb Z}^{9}\oplus{\mathbb Z}_2^{11} }[/math] | [math]\displaystyle{ {\mathbb Z}^{11} }[/math] |
| [math]\displaystyle{ r=8 }[/math] | [math]\displaystyle{ {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{9} }[/math] | [math]\displaystyle{ {\mathbb Z}^{9} }[/math] |
| [math]\displaystyle{ r=9 }[/math] | [math]\displaystyle{ {\mathbb Z}^{3}\oplus{\mathbb Z}_2^{5} }[/math] | [math]\displaystyle{ {\mathbb Z}^{5} }[/math] |
| [math]\displaystyle{ r=10 }[/math] | [math]\displaystyle{ {\mathbb Z}\oplus{\mathbb Z}_2^{3} }[/math] | [math]\displaystyle{ {\mathbb Z}^{3} }[/math] |
| [math]\displaystyle{ r=11 }[/math] | [math]\displaystyle{ {\mathbb Z}_2 }[/math] | [math]\displaystyle{ {\mathbb Z} }[/math] |
