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

Latest revision as of 08:00, 27 June 2006

$\dim {\mathcal {G}}_{2r+i}\operatorname {KH} _{\mathbb {Z} }^{r}$	$i=17$	$i=19$	$i=21$	$i=23$	$i=25$	$i=27$	$i=29$	$i=31$
$r=0$							${\mathbb {Z} }$	${\mathbb {Z} }$
$r=1$
$r=2$							${\mathbb {Z} }$
$r=3$							${\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=4$						${\mathbb {Z} }$	${\mathbb {Z} }$
$r=5$							${\mathbb {Z} }$	${\mathbb {Z} }$
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r=6}					${\mathbb {Z} }$	${\mathbb {Z} }$
$r=7$					${\mathbb {Z} }_{2}$	${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=8$				${\mathbb {Z} }$	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\mathbb Z}^{2}}
$r=9$					${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }^{2}$
$r=10$			${\mathbb {Z} }$	${\mathbb {Z} }^{2}$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }_{2}$
$r=11$			${\mathbb {Z} }_{2}$	${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}^{2}$	${\mathbb {Z} }^{3}$
$r=12$			${\mathbb {Z} }^{2}$	${\mathbb {Z} }$	${\mathbb {Z} }_{2}\oplus {\mathbb {Z} }_{5}$	${\mathbb {Z} }$
$r=13$			${\mathbb {Z} }_{2}^{2}$	${\mathbb {Z} }^{3}\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=14$		${\mathbb {Z} }$	${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }_{2}^{2}$	${\mathbb {Z} }$
$r=15$		${\mathbb {Z} }_{2}$	${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }^{2}$
$r=16$	${\mathbb {Z} }$	${\mathbb {Z} }$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=17$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=18$	${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }_{2}^{2}$	${\mathbb {Z} }_{4}$
$r=19$	${\mathbb {Z} }_{2}\oplus {\mathbb {Z} }_{3}$	${\mathbb {Z} }$
$r=20$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }_{2}\oplus {\mathbb {Z} }_{3}$	${\mathbb {Z} }_{3}$
$r=21$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }_{2}$

@@ Line 1: / Line 1: @@
 {| border=1 cellspacing=0 cellpadding=1
 |- align=center
-|<math>\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}(T(7,6))</math>
+|<math>\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}</math>
 |<math>i=17</math>
 |<math>i=19</math>
@@ Line 18: / Line 18: @@
 |
 |
-|<math>{\color{black}\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
-|<math>{\color{black}\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
 |- align=center
 |<math>r=1</math>
@@ Line 38: / Line 38: @@
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-|<math>{\color{black}\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
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 |- align=center
@@ Line 48: / Line 48: @@
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-|<math>{\color{black}\mathbb Z}_2</math>
+|<math>{\mathbb Z}_2</math>
-|<math>{\color{black}\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
 |- align=center
 |<math>r=4</math>
@@ Line 57: / Line 57: @@
 |
 |
-|<math>{\color{black}\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
-|<math>{\color{black}\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
 |
 |- align=center
@@ Line 68: / Line 68: @@
 |
 |
-|<math>{\color{black}\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
-|<math>{\color{black}\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
 |- align=center
 |<math>r=6</math>
@@ Line 76: / Line 76: @@
 |
 |
-|<math>{\color{black}\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
-|<math>{\color{black}\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
 |
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@@ Line 86: / Line 86: @@
 |
 |
-|<math>{\color{black}\mathbb Z}_2</math>
+|<math>{\mathbb Z}_2</math>
-|<math>{\color{black}\mathbb Z}\oplus{\color{black}\mathbb Z}_2</math>
+|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
-|<math>{\color{black}\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
 |
 |- align=center
@@ Line 95: / Line 95: @@
 |bgcolor=yellow|
 |
-|<math>{\color{black}\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
-|<math>{\color{black}\mathbb Z}^2</math>
+|<math>{\mathbb Z}^{2}</math>
 |
 |
@@ Line 106: / Line 106: @@
 |
 |
-|<math>{\color{black}\mathbb Z}\oplus{\color{black}\mathbb Z}_2</math>
+|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
-|<math>{\color{black}\mathbb Z}^2</math>
+|<math>{\mathbb Z}^{2}</math>
 |
 |
@@ Line 114: / Line 114: @@
 |bgcolor=yellow|
 |bgcolor=yellow|
-|<math>{\color{black}\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
-|<math>{\color{black}\mathbb Z}^2</math>
+|<math>{\mathbb Z}^{2}</math>
-|<math>{\color{black}\mathbb Z}_2</math>
+|<math>{\mathbb Z}_2</math>
-|<math>{\color{black}\mathbb Z}_2</math>
+|<math>{\mathbb Z}_2</math>
 |
 |
@@ Line 124: / Line 124: @@
 |bgcolor=yellow|
 |bgcolor=yellow|
-|<math>{\color{black}\mathbb Z}_2</math>
+|<math>{\mathbb Z}_2</math>
-|<math>{\color{black}\mathbb Z}\oplus{\color{black}\mathbb Z}_2^2</math>
+|<math>{\mathbb Z}\oplus{\mathbb Z}_2^{2}</math>
-|<math>{\color{black}\mathbb Z}^3</math>
+|<math>{\mathbb Z}^{3}</math>
 |
 |
@@ Line 134: / Line 134: @@
 |bgcolor=yellow|
 |bgcolor=yellow|
-|<math>{\color{black}\mathbb Z}^2</math>
+|<math>{\mathbb Z}^{2}</math>
-|<math>{\color{black}\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
-|<math>{\color{black}\mathbb Z}_2\oplus{\color{black}\mathbb Z}_5</math>
+|<math>{\mathbb Z}_2\oplus{\mathbb Z}_5</math>
-|<math>{\color{black}\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
 |
 |
@@ Line 144: / Line 144: @@
 |bgcolor=yellow|
 |bgcolor=yellow|
-|<math>{\color{black}\mathbb Z}_2^2</math>
+|<math>{\mathbb Z}_2^{2}</math>
-|<math>{\color{black}\mathbb Z}^3\oplus{\color{black}\mathbb Z}_2</math>
+|<math>{\mathbb Z}^{3}\oplus{\mathbb Z}_2</math>
-|<math>{\color{black}\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
 |
 |
@@ Line 153: / Line 153: @@
 |<math>r=14</math>
 |bgcolor=yellow|
-|bgcolor=yellow|<math>{\color{black}\mathbb Z}</math>
+|bgcolor=yellow|<math>{\mathbb Z}</math>
-|<math>{\color{black}\mathbb Z}\oplus{\color{black}\mathbb Z}_2</math>
+|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
-|<math>{\color{black}\mathbb Z}_2^2</math>
+|<math>{\mathbb Z}_2^{2}</math>
-|<math>{\color{black}\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
 |
 |
@@ Line 163: / Line 163: @@
 |<math>r=15</math>
 |bgcolor=yellow|
-|bgcolor=yellow|<math>{\color{black}\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}_2</math>
-|<math>{\color{black}\mathbb Z}^2\oplus{\color{black}\mathbb Z}_2</math>
+|<math>{\mathbb Z}^{2}\oplus{\mathbb Z}_2</math>
-|<math>{\color{black}\mathbb Z}^2</math>
+|<math>{\mathbb Z}^{2}</math>
 |
 |
@@ Line 172: / Line 172: @@
 |- align=center
 |<math>r=16</math>
-|bgcolor=yellow|<math>{\color{black}\mathbb Z}</math>
+|bgcolor=yellow|<math>{\mathbb Z}</math>
-|bgcolor=yellow|<math>{\color{black}\mathbb Z}</math>
+|bgcolor=yellow|<math>{\mathbb Z}</math>
-|<math>{\color{black}\mathbb Z}_2</math>
+|<math>{\mathbb Z}_2</math>
-|<math>{\color{black}\mathbb Z}\oplus{\color{black}\mathbb Z}_2</math>
+|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
-|<math>{\color{black}\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
 |
 |
@@ Line 182: / Line 182: @@
 |- align=center
 |<math>r=17</math>
-|bgcolor=yellow|<math>{\color{black}\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}_2</math>
-|bgcolor=yellow|<math>{\color{black}\mathbb Z}\oplus{\color{black}\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
-|<math>{\color{black}\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
 |
 |
@@ Line 192: / Line 192: @@
 |- align=center
 |<math>r=18</math>
-|bgcolor=yellow|<math>{\color{black}\mathbb Z}\oplus{\color{black}\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
-|bgcolor=yellow|<math>{\color{black}\mathbb Z}_2^2</math>
+|bgcolor=yellow|<math>{\mathbb Z}_2^{2}</math>
-|<math>{\color{black}\mathbb Z}_4</math>
+|<math>{\mathbb Z}_4</math>
 |
 |
@@ Line 202: / Line 202: @@
 |- align=center
 |<math>r=19</math>
-|bgcolor=yellow|<math>{\color{black}\mathbb Z}_2\oplus{\color{red}\mathbb Z}_3</math>
+|bgcolor=yellow|<math>{\mathbb Z}_2\oplus{\mathbb Z}_3</math>
-|bgcolor=yellow|<math>{\color{black}\mathbb Z}</math>
+|bgcolor=yellow|<math>{\mathbb Z}</math>
 |
 |
@@ Line 212: / Line 212: @@
 |- align=center
 |<math>r=20</math>
-|bgcolor=yellow|<math>{\color{black}\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}_2</math>
-|bgcolor=yellow|<math>{\color{black}\mathbb Z}_2\oplus{\color{red}\mathbb Z}_3</math>
+|bgcolor=yellow|<math>{\mathbb Z}_2\oplus{\mathbb Z}_3</math>
-|<math>{\color{red}\mathbb Z}_3</math>
+|<math>{\mathbb Z}_3</math>
 |
 |
@@ Line 222: / Line 222: @@
 |- align=center
 |<math>r=21</math>
-|bgcolor=yellow|<math>{\color{black}\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}_2</math>
-|bgcolor=yellow|<math>{\color{black}\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}_2</math>
 |
 |

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

Latest revision as of 08:00, 27 June 2006

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