Data:K11a284/Integral Khovanov Homology: Difference between revisions
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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}^4\oplus{\mathbb Z}_2</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{4}\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=-2</math> |
|<math>r=-2</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^8\oplus{\mathbb Z}_2^4</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{8}\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=-1</math> |
|<math>r=-1</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^11\oplus{\mathbb Z}_2^8</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{11}\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=0</math> |
|<math>r=0</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^15\oplus{\mathbb Z}_2^11</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{15}\oplus{\mathbb Z}_2^{11}</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}^15\oplus{\mathbb Z}_2^14</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{15}\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=2</math> |
|<math>r=2</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^14\oplus{\mathbb Z}_2^15</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{14}\oplus{\mathbb Z}_2^{15}</math> |
||
|bgcolor=yellow|<math>{\mathbb Z}^15</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{15}</math> |
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|- align=center |
|- align=center |
||
|<math>r=3</math> |
|<math>r=3</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^11\oplus{\mathbb Z}_2^14</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{11}\oplus{\mathbb Z}_2^{14}</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=4</math> |
|<math>r=4</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^7\oplus{\mathbb Z}_2^11</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{7}\oplus{\mathbb Z}_2^{11}</math> |
||
|bgcolor=yellow|<math>{\mathbb Z}^11</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{11}</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}^3\oplus{\mathbb Z}_2^7</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{3}\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=6</math> |
|<math>r=6</math> |
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|bgcolor=yellow|<math>{\mathbb Z}\oplus{\mathbb Z}_2^3</math> |
|bgcolor=yellow|<math>{\mathbb Z}\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=7</math> |
|<math>r=7</math> |
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Latest revision as of 08:17, 27 June 2006
| [math]\displaystyle{ \dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} }[/math] | [math]\displaystyle{ i=1 }[/math] | [math]\displaystyle{ i=3 }[/math] |
| [math]\displaystyle{ r=-4 }[/math] | [math]\displaystyle{ {\mathbb Z} }[/math] | |
| [math]\displaystyle{ r=-3 }[/math] | [math]\displaystyle{ {\mathbb Z}^{4}\oplus{\mathbb Z}_2 }[/math] | [math]\displaystyle{ {\mathbb Z} }[/math] |
| [math]\displaystyle{ r=-2 }[/math] | [math]\displaystyle{ {\mathbb Z}^{8}\oplus{\mathbb Z}_2^{4} }[/math] | [math]\displaystyle{ {\mathbb Z}^{4} }[/math] |
| [math]\displaystyle{ r=-1 }[/math] | [math]\displaystyle{ {\mathbb Z}^{11}\oplus{\mathbb Z}_2^{8} }[/math] | [math]\displaystyle{ {\mathbb Z}^{8} }[/math] |
| [math]\displaystyle{ r=0 }[/math] | [math]\displaystyle{ {\mathbb Z}^{15}\oplus{\mathbb Z}_2^{11} }[/math] | [math]\displaystyle{ {\mathbb Z}^{12} }[/math] |
| [math]\displaystyle{ r=1 }[/math] | [math]\displaystyle{ {\mathbb Z}^{15}\oplus{\mathbb Z}_2^{14} }[/math] | [math]\displaystyle{ {\mathbb Z}^{14} }[/math] |
| [math]\displaystyle{ r=2 }[/math] | [math]\displaystyle{ {\mathbb Z}^{14}\oplus{\mathbb Z}_2^{15} }[/math] | [math]\displaystyle{ {\mathbb Z}^{15} }[/math] |
| [math]\displaystyle{ r=3 }[/math] | [math]\displaystyle{ {\mathbb Z}^{11}\oplus{\mathbb Z}_2^{14} }[/math] | [math]\displaystyle{ {\mathbb Z}^{14} }[/math] |
| [math]\displaystyle{ r=4 }[/math] | [math]\displaystyle{ {\mathbb Z}^{7}\oplus{\mathbb Z}_2^{11} }[/math] | [math]\displaystyle{ {\mathbb Z}^{11} }[/math] |
| [math]\displaystyle{ r=5 }[/math] | [math]\displaystyle{ {\mathbb Z}^{3}\oplus{\mathbb Z}_2^{7} }[/math] | [math]\displaystyle{ {\mathbb Z}^{7} }[/math] |
| [math]\displaystyle{ r=6 }[/math] | [math]\displaystyle{ {\mathbb Z}\oplus{\mathbb Z}_2^{3} }[/math] | [math]\displaystyle{ {\mathbb Z}^{3} }[/math] |
| [math]\displaystyle{ r=7 }[/math] | [math]\displaystyle{ {\mathbb Z}_2 }[/math] | [math]\displaystyle{ {\mathbb Z} }[/math] |
