Data:10 86/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=-1</math> |
|<math>i=-1</math> |
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|<math>i=1</math> |
|<math>i=1</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}^3\oplus{\mathbb Z}_2</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{3}\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}^5\oplus{\mathbb Z}_2^3</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{5}\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=-1</math> |
|<math>r=-1</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^6\oplus{\mathbb Z}_2^5</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{6}\oplus{\mathbb Z}_2^{5}</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^5</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{5}</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}^8\oplus{\mathbb Z}_2^6</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{8}\oplus{\mathbb Z}_2^{6}</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=1</math> |
|<math>r=1</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^7\oplus{\mathbb Z}_2^7</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{7}\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 |
||
|<math>r=2</math> |
|<math>r=2</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^6\oplus{\mathbb Z}_2^7</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{6}\oplus{\mathbb Z}_2^{7}</math> |
||
|bgcolor=yellow|<math>{\mathbb Z}^7</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{7}</math> |
||
|- align=center |
|- align=center |
||
|<math>r=3</math> |
|<math>r=3</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^4\oplus{\mathbb Z}_2^6</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{4}\oplus{\mathbb Z}_2^{6}</math> |
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|bgcolor=yellow|<math>{\mathbb Z}^6</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{6}</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}^2\oplus{\mathbb Z}_2^4</math> |
|bgcolor=yellow|<math>{\mathbb Z}^{2}\oplus{\mathbb Z}_2^{4}</math> |
||
|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=5</math> |
|<math>r=5</math> |
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|bgcolor=yellow|<math>{\mathbb Z}\oplus{\mathbb Z}_2^2</math> |
|bgcolor=yellow|<math>{\mathbb Z}\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=6</math> |
|<math>r=6</math> |