Data:T(7,6)/Integral Khovanov Homology: Difference between revisions

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{| border=1
{| border=1 cellspacing=0 cellpadding=1
|- align=center
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|<math>\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}</math>
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|<math>j=17</math>
|<math>i=17</math>
|<math>j=19</math>
|<math>i=19</math>
|<math>j=21</math>
|<math>i=21</math>
|<math>j=23</math>
|<math>i=23</math>
|<math>j=25</math>
|<math>i=25</math>
|<math>j=27</math>
|<math>i=27</math>
|<math>j=29</math>
|<math>i=29</math>
|<math>j=31</math>
|<math>i=31</math>
|- align=center
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|<math>r=0</math>
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|<math>r=7</math>
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|<math>r=8</math>
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|<math>{\mathbb Z}</math>
|<math>{\mathbb Z}</math>
|<math>{\mathbb Z}^2</math>
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|<math>r=9</math>
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|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
|<math>{\mathbb Z}^2</math>
|<math>{\mathbb Z}^{2}</math>
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|- align=center
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|<math>r=10</math>
|<math>r=10</math>
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|<math>{\mathbb Z}</math>
|<math>{\mathbb Z}</math>
|<math>{\mathbb Z}^2</math>
|<math>{\mathbb Z}^{2}</math>
|<math>{\mathbb Z}_2</math>
|<math>{\mathbb Z}_2</math>
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|- align=center
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|<math>r=11</math>
|<math>r=11</math>
|bgcolor=yellow|
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|<math>{\mathbb Z}_2</math>
|<math>{\mathbb Z}_2</math>
|<math>{\mathbb Z}\oplus{\mathbb Z}_2^2</math>
|<math>{\mathbb Z}\oplus{\mathbb Z}_2^{2}</math>
|<math>{\mathbb Z}^3</math>
|<math>{\mathbb Z}^{3}</math>
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|- align=center
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|<math>r=12</math>
|<math>r=12</math>
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|<math>{\mathbb Z}^2</math>
|<math>{\mathbb Z}^{2}</math>
|<math>{\mathbb Z}</math>
|<math>{\mathbb Z}</math>
|<math>{\mathbb Z}_2\oplus{\mathbb Z}_5</math>
|<math>{\mathbb Z}_2\oplus{\mathbb Z}_5</math>
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|- align=center
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|<math>r=13</math>
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|<math>{\mathbb Z}_2^2</math>
|<math>{\mathbb Z}_2^{2}</math>
|<math>{\mathbb Z}^3\oplus{\mathbb Z}_2</math>
|<math>{\mathbb Z}^{3}\oplus{\mathbb Z}_2</math>
|<math>{\mathbb Z}</math>
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|<math>r=14</math>
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|<math>{\mathbb Z}</math>
|bgcolor=yellow|<math>{\mathbb Z}</math>
|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
|<math>{\mathbb Z}_2^2</math>
|<math>{\mathbb Z}_2^{2}</math>
|<math>{\mathbb Z}</math>
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|<math>r=15</math>
|<math>r=15</math>
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|<math>{\mathbb Z}_2</math>
|bgcolor=yellow|<math>{\mathbb Z}_2</math>
|<math>{\mathbb Z}^2\oplus{\mathbb Z}_2</math>
|<math>{\mathbb Z}^{2}\oplus{\mathbb Z}_2</math>
|<math>{\mathbb Z}^2</math>
|<math>{\mathbb Z}^{2}</math>
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|- align=center
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|<math>r=16</math>
|<math>r=16</math>
|<math>{\mathbb Z}</math>
|bgcolor=yellow|<math>{\mathbb Z}</math>
|<math>{\mathbb Z}</math>
|bgcolor=yellow|<math>{\mathbb Z}</math>
|<math>{\mathbb Z}_2</math>
|<math>{\mathbb Z}_2</math>
|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
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|- align=center
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|<math>r=17</math>
|<math>r=17</math>
|<math>{\mathbb Z}_2</math>
|bgcolor=yellow|<math>{\mathbb Z}_2</math>
|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
|bgcolor=yellow|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
|<math>{\mathbb Z}</math>
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|- align=center
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|<math>r=18</math>
|<math>r=18</math>
|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
|bgcolor=yellow|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
|<math>{\mathbb Z}_2^2</math>
|bgcolor=yellow|<math>{\mathbb Z}_2^{2}</math>
|<math>{\mathbb Z}_4</math>
|<math>{\mathbb Z}_4</math>
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|- align=center
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|<math>r=19</math>
|<math>r=19</math>
|<math>{\mathbb Z}_2\oplus{\mathbb Z}_3</math>
|bgcolor=yellow|<math>{\mathbb Z}_2\oplus{\mathbb Z}_3</math>
|<math>{\mathbb Z}</math>
|bgcolor=yellow|<math>{\mathbb Z}</math>
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|- align=center
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|<math>r=20</math>
|<math>r=20</math>
|<math>{\mathbb Z}_2</math>
|bgcolor=yellow|<math>{\mathbb Z}_2</math>
|<math>{\mathbb Z}_2\oplus{\mathbb Z}_3</math>
|bgcolor=yellow|<math>{\mathbb Z}_2\oplus{\mathbb Z}_3</math>
|<math>{\mathbb Z}_3</math>
|<math>{\mathbb Z}_3</math>
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|- align=center
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|<math>r=21</math>
|<math>r=21</math>
|<math>{\mathbb Z}_2</math>
|bgcolor=yellow|<math>{\mathbb Z}_2</math>
|<math>{\mathbb Z}_2</math>
|bgcolor=yellow|<math>{\mathbb Z}_2</math>
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Latest revision as of 09:00, 27 June 2006

[math]\displaystyle{ \dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} }[/math] [math]\displaystyle{ i=17 }[/math] [math]\displaystyle{ i=19 }[/math] [math]\displaystyle{ i=21 }[/math] [math]\displaystyle{ i=23 }[/math] [math]\displaystyle{ i=25 }[/math] [math]\displaystyle{ i=27 }[/math] [math]\displaystyle{ i=29 }[/math] [math]\displaystyle{ i=31 }[/math]
[math]\displaystyle{ r=0 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=1 }[/math]
[math]\displaystyle{ r=2 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=3 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=4 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=5 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=6 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=7 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}\oplus{\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=8 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math] [math]\displaystyle{ {\mathbb Z}^{2} }[/math]
[math]\displaystyle{ r=9 }[/math] [math]\displaystyle{ {\mathbb Z}\oplus{\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}^{2} }[/math]
[math]\displaystyle{ r=10 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math] [math]\displaystyle{ {\mathbb Z}^{2} }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math]
[math]\displaystyle{ r=11 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}\oplus{\mathbb Z}_2^{2} }[/math] [math]\displaystyle{ {\mathbb Z}^{3} }[/math]
[math]\displaystyle{ r=12 }[/math] [math]\displaystyle{ {\mathbb Z}^{2} }[/math] [math]\displaystyle{ {\mathbb Z} }[/math] [math]\displaystyle{ {\mathbb Z}_2\oplus{\mathbb Z}_5 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=13 }[/math] [math]\displaystyle{ {\mathbb Z}_2^{2} }[/math] [math]\displaystyle{ {\mathbb Z}^{3}\oplus{\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=14 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math] [math]\displaystyle{ {\mathbb Z}\oplus{\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}_2^{2} }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=15 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}^{2}\oplus{\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}^{2} }[/math]
[math]\displaystyle{ r=16 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math] [math]\displaystyle{ {\mathbb Z} }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}\oplus{\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=17 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}\oplus{\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=18 }[/math] [math]\displaystyle{ {\mathbb Z}\oplus{\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}_2^{2} }[/math] [math]\displaystyle{ {\mathbb Z}_4 }[/math]
[math]\displaystyle{ r=19 }[/math] [math]\displaystyle{ {\mathbb Z}_2\oplus{\mathbb Z}_3 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=20 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}_2\oplus{\mathbb Z}_3 }[/math] [math]\displaystyle{ {\mathbb Z}_3 }[/math]
[math]\displaystyle{ r=21 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math]
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