Data:T(5,3)/Integral Khovanov Homology: Difference between revisions

Latest revision as of 08:10, 27 June 2006

$\dim {\mathcal {G}}_{2r+i}\operatorname {KH} _{\mathbb {Z} }^{r}$	$i=5$	$i=7$	$i=9$
$r=0$		${\mathbb {Z} }$	${\mathbb {Z} }$
$r=1$
$r=2$		${\mathbb {Z} }$
$r=3$		${\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=4$	${\mathbb {Z} }$	${\mathbb {Z} }$
$r=5$		${\mathbb {Z} }$	${\mathbb {Z} }$
$r=6$	${\mathbb {Z} }$
$r=7$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }$

@@ Line 1: / Line 1: @@
+{| border=1 cellspacing=0 cellpadding=1
-<math>t^7 \textrm{ZMod}(0) q^{21}+t^5 \textrm{ZMod}(0) q^{19}+t^7 \textrm{ZMod}(2) q^{19}+t^6 \textrm{ZMod}(0) q^{17}+t^5 \textrm{ZMod}(0) q^{17}+t^4 \textrm{ZMod}(0) q^{15}+t^3 \textrm{ZMod}(0) q^{15}+t^4 \textrm{ZMod}(0) q^{13}+t^3 \textrm{ZMod}(2) q^{13}+t^2 \textrm{ZMod}(0) q^{11}+\textrm{ZMod}(0) q^9+\textrm{ZMod}(0) q^7</math>
+|- align=center
+|<math>\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}</math>
+|<math>i=5</math>
+|<math>i=7</math>
+|<math>i=9</math>
+|- align=center
+|<math>r=0</math>
+|
+|bgcolor=yellow|<math>{\mathbb Z}</math>
+|bgcolor=yellow|<math>{\mathbb Z}</math>
+|- align=center
+|<math>r=1</math>
+|
+|bgcolor=yellow|
+|bgcolor=yellow|
+|- align=center
+|<math>r=2</math>
+|
+|bgcolor=yellow|<math>{\mathbb Z}</math>
+|bgcolor=yellow|
+|- align=center
+|<math>r=3</math>
+|
+|bgcolor=yellow|<math>{\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}</math>
+|- align=center
+|<math>r=4</math>
+|<math>{\mathbb Z}</math>
+|bgcolor=yellow|<math>{\mathbb Z}</math>
+|bgcolor=yellow|
+|- align=center
+|<math>r=5</math>
+|
+|bgcolor=yellow|<math>{\mathbb Z}</math>
+|bgcolor=yellow|<math>{\mathbb Z}</math>
+|- align=center
+|<math>r=6</math>
+|<math>{\mathbb Z}</math>
+|bgcolor=yellow|
+|bgcolor=yellow|
+|- align=center
+|<math>r=7</math>
+|<math>{\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}</math>
+|bgcolor=yellow|
+|}