Data:L11a41/Integral Khovanov Homology: Difference between revisions
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|- align=center |
|- align=center |
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|<math>r=-6</math> |
|<math>r=-6</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^2\oplus{\mathbb Z}_2</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{2}\oplus{\mathbb Z}_2</math> |
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|bgcolor=yellow|<math>{\mathbb Z}</math> |
|bgcolor=yellow|<math>{\mathbb Z}</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}^6\oplus{\mathbb Z}_2^2</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{6}\oplus{\mathbb Z}_2^{2}</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^2</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{2}</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}^9\oplus{\mathbb Z}_2^6</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{9}\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=-3</math> |
|<math>r=-3</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^12\oplus{\mathbb Z}_2^9</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{12}\oplus{\mathbb Z}_2^{9}</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^9</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{9}</math> |
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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}^14\oplus{\mathbb Z}_2^12</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{14}\oplus{\mathbb Z}_2^{12}</math> |
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|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=-1</math> |
|<math>r=-1</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^12\oplus{\mathbb Z}_2^14</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{12}\oplus{\mathbb Z}_2^{14}</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^14</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{14}</math> |
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|- align=center |
|- align=center |
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|<math>r=0</math> |
|<math>r=0</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^12\oplus{\mathbb Z}_2^12</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{12}\oplus{\mathbb Z}_2^{12}</math> |
||
|bgcolor=yellow|<math>{\mathbb Z}^14</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{14}</math> |
||
|- 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}^8\oplus{\mathbb Z}_2^10</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{8}\oplus{\mathbb Z}_2^{10}</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^10</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{10}</math> |
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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}^4\oplus{\mathbb Z}_2^8</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{4}\oplus{\mathbb Z}_2^{8}</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^8</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{8}</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}\oplus{\mathbb Z}_2^4</math> |
|bgcolor=yellow|<math>{\mathbb Z}\oplus{\mathbb Z}_2^{4}</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^4</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{4}</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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Latest revision as of 08:39, 27 June 2006
| [math]\displaystyle{ \dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} }[/math] | [math]\displaystyle{ i=-2 }[/math] | [math]\displaystyle{ i=0 }[/math] |
| [math]\displaystyle{ r=-7 }[/math] | [math]\displaystyle{ {\mathbb Z} }[/math] | |
| [math]\displaystyle{ r=-6 }[/math] | [math]\displaystyle{ {\mathbb Z}^{2}\oplus{\mathbb Z}_2 }[/math] | [math]\displaystyle{ {\mathbb Z} }[/math] |
| [math]\displaystyle{ r=-5 }[/math] | [math]\displaystyle{ {\mathbb Z}^{6}\oplus{\mathbb Z}_2^{2} }[/math] | [math]\displaystyle{ {\mathbb Z}^{2} }[/math] |
| [math]\displaystyle{ r=-4 }[/math] | [math]\displaystyle{ {\mathbb Z}^{9}\oplus{\mathbb Z}_2^{6} }[/math] | [math]\displaystyle{ {\mathbb Z}^{6} }[/math] |
| [math]\displaystyle{ r=-3 }[/math] | [math]\displaystyle{ {\mathbb Z}^{12}\oplus{\mathbb Z}_2^{9} }[/math] | [math]\displaystyle{ {\mathbb Z}^{9} }[/math] |
| [math]\displaystyle{ r=-2 }[/math] | [math]\displaystyle{ {\mathbb Z}^{14}\oplus{\mathbb Z}_2^{12} }[/math] | [math]\displaystyle{ {\mathbb Z}^{12} }[/math] |
| [math]\displaystyle{ r=-1 }[/math] | [math]\displaystyle{ {\mathbb Z}^{12}\oplus{\mathbb Z}_2^{14} }[/math] | [math]\displaystyle{ {\mathbb Z}^{14} }[/math] |
| [math]\displaystyle{ r=0 }[/math] | [math]\displaystyle{ {\mathbb Z}^{12}\oplus{\mathbb Z}_2^{12} }[/math] | [math]\displaystyle{ {\mathbb Z}^{14} }[/math] |
| [math]\displaystyle{ r=1 }[/math] | [math]\displaystyle{ {\mathbb Z}^{8}\oplus{\mathbb Z}_2^{10} }[/math] | [math]\displaystyle{ {\mathbb Z}^{10} }[/math] |
| [math]\displaystyle{ r=2 }[/math] | [math]\displaystyle{ {\mathbb Z}^{4}\oplus{\mathbb Z}_2^{8} }[/math] | [math]\displaystyle{ {\mathbb Z}^{8} }[/math] |
| [math]\displaystyle{ r=3 }[/math] | [math]\displaystyle{ {\mathbb Z}\oplus{\mathbb Z}_2^{4} }[/math] | [math]\displaystyle{ {\mathbb Z}^{4} }[/math] |
| [math]\displaystyle{ r=4 }[/math] | [math]\displaystyle{ {\mathbb Z}_2 }[/math] | [math]\displaystyle{ {\mathbb Z} }[/math] |
