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

Latest revision as of 08:00, 27 June 2006

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

@@ Line 1: / Line 1: @@
-{| border=1
+{| border=1 cellspacing=0 cellpadding=1
 |- align=center
+|<math>\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}</math>
-|
-|<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
 |<math>r=0</math>
-|bgcolor=yellow||
+|bgcolor=yellow|
-|bgcolor=yellow||
+|bgcolor=yellow|
 |
 |
@@ Line 22: / Line 22: @@
 |- align=center
 |<math>r=1</math>
-|bgcolor=yellow||
+|bgcolor=yellow|
-|bgcolor=yellow||
+|bgcolor=yellow|
 |
 |
@@ Line 32: / Line 32: @@
 |- align=center
 |<math>r=2</math>
-|bgcolor=yellow||
+|bgcolor=yellow|
-|bgcolor=yellow||
+|bgcolor=yellow|
 |
 |
@@ Line 42: / Line 42: @@
 |- align=center
 |<math>r=3</math>
-|bgcolor=yellow||
+|bgcolor=yellow|
-|bgcolor=yellow||
+|bgcolor=yellow|
 |
 |
@@ Line 52: / Line 52: @@
 |- align=center
 |<math>r=4</math>
-|bgcolor=yellow||
+|bgcolor=yellow|
-|bgcolor=yellow||
+|bgcolor=yellow|
 |
 |
@@ Line 62: / Line 62: @@
 |- align=center
 |<math>r=5</math>
-|bgcolor=yellow||
+|bgcolor=yellow|
-|bgcolor=yellow||
+|bgcolor=yellow|
 |
 |
@@ Line 72: / Line 72: @@
 |- align=center
 |<math>r=6</math>
-|bgcolor=yellow||
+|bgcolor=yellow|
-|bgcolor=yellow||
+|bgcolor=yellow|
 |
 |
@@ Line 82: / Line 82: @@
 |- align=center
 |<math>r=7</math>
-|bgcolor=yellow||
+|bgcolor=yellow|
-|bgcolor=yellow||
+|bgcolor=yellow|
 |
 |
@@ Line 92: / Line 92: @@
 |- align=center
 |<math>r=8</math>
-|bgcolor=yellow||
+|bgcolor=yellow|
-|bgcolor=yellow||
+|bgcolor=yellow|
 |
 |<math>{\mathbb Z}</math>
-|<math>{\mathbb Z}^2</math>
+|<math>{\mathbb Z}^{2}</math>
 |
 |
@@ Line 102: / Line 102: @@
 |- align=center
 |<math>r=9</math>
-|bgcolor=yellow||
+|bgcolor=yellow|
-|bgcolor=yellow||
+|bgcolor=yellow|
 |
 |
 |<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
-|<math>{\mathbb Z}^2</math>
+|<math>{\mathbb Z}^{2}</math>
 |
 |
 |- align=center
 |<math>r=10</math>
-|bgcolor=yellow||
+|bgcolor=yellow|
-|bgcolor=yellow||
+|bgcolor=yellow|
 |<math>{\mathbb Z}</math>
-|<math>{\mathbb Z}^2</math>
+|<math>{\mathbb Z}^{2}</math>
 |<math>{\mathbb Z}_2</math>
 |<math>{\mathbb Z}_2</math>
@@ Line 122: / Line 122: @@
 |- align=center
 |<math>r=11</math>
-|bgcolor=yellow||
+|bgcolor=yellow|
-|bgcolor=yellow||
+|bgcolor=yellow|
 |<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>
 |
 |
@@ Line 132: / Line 132: @@
 |- align=center
 |<math>r=12</math>
-|bgcolor=yellow||
+|bgcolor=yellow|
-|bgcolor=yellow||
+|bgcolor=yellow|
-|<math>{\mathbb Z}^2</math>
+|<math>{\mathbb Z}^{2}</math>
 |<math>{\mathbb Z}</math>
 |<math>{\mathbb Z}_2\oplus{\mathbb Z}_5</math>
@@ Line 142: / Line 142: @@
 |- align=center
 |<math>r=13</math>
-|bgcolor=yellow||
+|bgcolor=yellow|
-|bgcolor=yellow||
+|bgcolor=yellow|
-|<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>
 |
@@ Line 152: / Line 152: @@
 |- align=center
 |<math>r=14</math>
-|bgcolor=yellow||
+|bgcolor=yellow|
-|bgcolor=yellow||<math>{\mathbb Z}</math>
+|bgcolor=yellow|<math>{\mathbb Z}</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>
 |
@@ Line 162: / Line 162: @@
 |- align=center
 |<math>r=15</math>
-|bgcolor=yellow||
+|bgcolor=yellow|
-|bgcolor=yellow||<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>
 |
 |
@@ Line 172: / Line 172: @@
 |- align=center
 |<math>r=16</math>
-|bgcolor=yellow||<math>{\mathbb Z}</math>
+|bgcolor=yellow|<math>{\mathbb Z}</math>
-|bgcolor=yellow||<math>{\mathbb Z}</math>
+|bgcolor=yellow|<math>{\mathbb Z}</math>
 |<math>{\mathbb Z}_2</math>
 |<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
@@ Line 182: / Line 182: @@
 |- align=center
 |<math>r=17</math>
-|bgcolor=yellow||<math>{\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}_2</math>
-|bgcolor=yellow||<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
 |<math>{\mathbb Z}</math>
 |
@@ Line 192: / Line 192: @@
 |- align=center
 |<math>r=18</math>
-|bgcolor=yellow||<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
-|bgcolor=yellow||<math>{\mathbb Z}_2^2</math>
+|bgcolor=yellow|<math>{\mathbb Z}_2^{2}</math>
 |<math>{\mathbb Z}_4</math>
 |
@@ Line 202: / Line 202: @@
 |- align=center
 |<math>r=19</math>
-|bgcolor=yellow||<math>{\mathbb Z}_2\oplus{\mathbb Z}_3</math>
+|bgcolor=yellow|<math>{\mathbb Z}_2\oplus{\mathbb Z}_3</math>
-|bgcolor=yellow||<math>{\mathbb Z}</math>
+|bgcolor=yellow|<math>{\mathbb Z}</math>
 |
 |
@@ Line 212: / Line 212: @@
 |- align=center
 |<math>r=20</math>
-|bgcolor=yellow||<math>{\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}_2</math>
-|bgcolor=yellow||<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>
 |
@@ Line 222: / Line 222: @@
 |- align=center
 |<math>r=21</math>
-|bgcolor=yellow||<math>{\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}_2</math>
-|bgcolor=yellow||<math>{\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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