Data:T(9,5)/Integral Khovanov Homology: Difference between revisions

Latest revision as of 08:01, 27 June 2006

$\dim {\mathcal {G}}_{2r+i}\operatorname {KH} _{\mathbb {Z} }^{r}$	$i=19$	$i=21$	$i=23$	$i=25$	$i=27$	$i=29$	$i=31$	$i=33$
$r=0$							${\mathbb {Z} }$	${\mathbb {Z} }$
$r=1$
$r=2$							${\mathbb {Z} }$
$r=3$							${\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=4$						${\mathbb {Z} }$	${\mathbb {Z} }$
$r=5$							${\mathbb {Z} }$	${\mathbb {Z} }$
$r=6$					${\mathbb {Z} }$	${\mathbb {Z} }$
$r=7$					${\mathbb {Z} }_{2}$	${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=8$				${\mathbb {Z} }$	${\mathbb {Z} }^{2}$
$r=9$					${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }^{2}$
$r=10$				${\mathbb {Z} }^{2}$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }_{2}$
$r=11$				${\mathbb {Z} }_{2}^{2}\oplus {\mathbb {Z} }_{5}$	${\mathbb {Z} }^{3}$
$r=12$			${\mathbb {Z} }^{2}$	${\mathbb {Z} }^{2}$	${\mathbb {Z} }_{2}\oplus {\mathbb {Z} }_{5}$	${\mathbb {Z} }$
$r=13$			${\mathbb {Z} }_{2}$	${\mathbb {Z} }^{3}\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }^{2}$
$r=14$		${\mathbb {Z} }$	${\mathbb {Z} }^{2}$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=15$		${\mathbb {Z} }_{2}$	${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}^{2}$	${\mathbb {Z} }^{3}$
$r=16$		${\mathbb {Z} }^{2}$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=17$		${\mathbb {Z} }_{2}\oplus {\mathbb {Z} }_{4}\oplus {\mathbb {Z} }_{5}$	${\mathbb {Z} }^{3}$
$r=18$	${\mathbb {Z} }$	${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }_{2}^{2}\oplus {\mathbb {Z} }_{5}$	${\mathbb {Z} }$
$r=19$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=20$	${\mathbb {Z} }$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=21$	${\mathbb {Z} }_{4}$	${\mathbb {Z} }$
$r=22$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }_{2}$

Data:T(9,5)/Integral Khovanov Homology: Difference between revisions

Latest revision as of 08:01, 27 June 2006

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+{| border=1 cellspacing=0 cellpadding=1
-<math>t^{22} \textrm{ZMod}(2) q^{65}+t^{21} \textrm{ZMod}(0) q^{63}+t^{20} \textrm{ZMod}(0) q^{63}+t^{22} \textrm{ZMod}(2) q^{63}+t^{19} \textrm{ZMod}(0) q^{61}+t^{18} \textrm{ZMod}(0) q^{61}+t^{20} \textrm{ZMod}(2) q^{61}+t^{21} \textrm{ZMod}(4) q^{61}+t^{20} \textrm{ZMod}(0) q^{59}+t^{16} \textrm{ZMod}(0) q^{59}+t^{19} \textrm{ZMod}(0,0,2) q^{59}+t^{18} \textrm{ZMod}(2,2,5) q^{59}+t^{19} \textrm{ZMod}(2) q^{57}+t^{18} \textrm{ZMod}(0,2) q^{57}+t^{16} \textrm{ZMod}(0,2) q^{57}+t^{17} \textrm{ZMod}(0,0,0) q^{57}+t^{18} \textrm{ZMod}(0) q^{55}+t^{14} \textrm{ZMod}(0) q^{55}+t^{16} \textrm{ZMod}(2) q^{55}+t^{15} \textrm{ZMod}(0,0,0) q^{55}+t^{17} \textrm{ZMod}(2,4,5) q^{55}+t^{12} \textrm{ZMod}(0) q^{53}+t^{14} \textrm{ZMod}(2) q^{53}+t^{16} \textrm{ZMod}(0,0) q^{53}+t^{13} \textrm{ZMod}(0,0) q^{53}+t^{15} \textrm{ZMod}(0,0,2,2) q^{53}+t^{15} \textrm{ZMod}(2) q^{51}+t^{14} \textrm{ZMod}(0,0) q^{51}+t^{12} \textrm{ZMod}(2,5) q^{51}+t^{13} \textrm{ZMod}(0,0,0,2) q^{51}+t^{14} \textrm{ZMod}(0) q^{49}+t^{13} \textrm{ZMod}(2) q^{49}+t^{10} \textrm{ZMod}(2) q^{49}+t^{12} \textrm{ZMod}(0,0) q^{49}+t^{11} \textrm{ZMod}(0,0,0) q^{49}+t^{10} \textrm{ZMod}(2) q^{47}+t^{12} \textrm{ZMod}(0,0) q^{47}+t^9 \textrm{ZMod}(0,0) q^{47}+t^{11} \textrm{ZMod}(2,2,5) q^{47}+t^7 \textrm{ZMod}(0) q^{45}+t^{10} \textrm{ZMod}(0,0) q^{45}+t^9 \textrm{ZMod}(0,2) q^{45}+t^5 \textrm{ZMod}(0) q^{43}+t^8 \textrm{ZMod}(0,0) q^{43}+t^7 \textrm{ZMod}(0,2) q^{43}+t^8 \textrm{ZMod}(0) q^{41}+t^6 \textrm{ZMod}(0) q^{41}+t^5 \textrm{ZMod}(0) q^{41}+t^7 \textrm{ZMod}(2) q^{41}+t^6 \textrm{ZMod}(0) q^{39}+t^4 \textrm{ZMod}(0) q^{39}+t^3 \textrm{ZMod}(0) q^{39}+t^4 \textrm{ZMod}(0) q^{37}+t^3 \textrm{ZMod}(2) q^{37}+t^2 \textrm{ZMod}(0) q^{35}+\textrm{ZMod}(0) q^{33}+\textrm{ZMod}(0) q^{31}</math>
+|- align=center
+|<math>\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}</math>
+|<math>i=19</math>
+|<math>i=21</math>
+|<math>i=23</math>
+|<math>i=25</math>
+|<math>i=27</math>
+|<math>i=29</math>
+|<math>i=31</math>
+|<math>i=33</math>
+|- align=center
+|<math>r=0</math>
+|
+|
+|bgcolor=yellow|
+|bgcolor=yellow|
+|
+|
+|<math>{\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
+|- align=center
+|<math>r=1</math>
+|
+|
+|bgcolor=yellow|
+|bgcolor=yellow|
+|
+|
+|
+|
+|- align=center
+|<math>r=2</math>
+|
+|
+|bgcolor=yellow|
+|bgcolor=yellow|
+|
+|
+|<math>{\mathbb Z}</math>
+|
+|- align=center
+|<math>r=3</math>
+|
+|
+|bgcolor=yellow|
+|bgcolor=yellow|
+|
+|
+|<math>{\mathbb Z}_2</math>
+|<math>{\mathbb Z}</math>
+|- align=center
+|<math>r=4</math>
+|
+|
+|bgcolor=yellow|
+|bgcolor=yellow|
+|
+|<math>{\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
+|
+|- align=center
+|<math>r=5</math>
+|
+|
+|bgcolor=yellow|
+|bgcolor=yellow|
+|
+|
+|<math>{\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
+|- align=center
+|<math>r=6</math>
+|
+|
+|bgcolor=yellow|
+|bgcolor=yellow|
+|<math>{\mathbb Z}</math>
+|<math>{\mathbb Z}</math>
+|
+|
+|- align=center
+|<math>r=7</math>
+|
+|
+|bgcolor=yellow|
+|bgcolor=yellow|
+|<math>{\mathbb Z}_2</math>
+|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
+|<math>{\mathbb Z}</math>
+|
+|- align=center
+|<math>r=8</math>
+|
+|
+|bgcolor=yellow|
+|bgcolor=yellow|<math>{\mathbb Z}</math>
+|<math>{\mathbb Z}^{2}</math>
+|
+|
+|
+|- align=center
+|<math>r=9</math>
+|
+|
+|bgcolor=yellow|
+|bgcolor=yellow|
+|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
+|<math>{\mathbb Z}^{2}</math>
+|
+|
+|- align=center
+|<math>r=10</math>
+|
+|
+|bgcolor=yellow|
+|bgcolor=yellow|<math>{\mathbb Z}^{2}</math>
+|<math>{\mathbb Z}_2</math>
+|<math>{\mathbb Z}_2</math>
+|
+|
+|- align=center
+|<math>r=11</math>
+|
+|
+|bgcolor=yellow|
+|bgcolor=yellow|<math>{\mathbb Z}_2^{2}\oplus{\mathbb Z}_5</math>
+|<math>{\mathbb Z}^{3}</math>
+|
+|
+|
+|- align=center
+|<math>r=12</math>
+|
+|
+|bgcolor=yellow|<math>{\mathbb Z}^{2}</math>
+|bgcolor=yellow|<math>{\mathbb Z}^{2}</math>
+|<math>{\mathbb Z}_2\oplus{\mathbb Z}_5</math>
+|<math>{\mathbb Z}</math>
+|
+|
+|- align=center
+|<math>r=13</math>
+|
+|
+|bgcolor=yellow|<math>{\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}^{3}\oplus{\mathbb Z}_2</math>
+|<math>{\mathbb Z}^{2}</math>
+|
+|
+|
+|- align=center
+|<math>r=14</math>
+|
+|<math>{\mathbb Z}</math>
+|bgcolor=yellow|<math>{\mathbb Z}^{2}</math>
+|bgcolor=yellow|<math>{\mathbb Z}_2</math>
+|<math>{\mathbb Z}</math>
+|
+|
+|
+|- align=center
+|<math>r=15</math>
+|
+|<math>{\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}^{2}\oplus{\mathbb Z}_2^{2}</math>
+|bgcolor=yellow|<math>{\mathbb Z}^{3}</math>
+|
+|
+|
+|
+|- align=center
+|<math>r=16</math>
+|
+|<math>{\mathbb Z}^{2}</math>
+|bgcolor=yellow|<math>{\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
+|<math>{\mathbb Z}</math>
+|
+|
+|
+|- align=center
+|<math>r=17</math>
+|
+|<math>{\mathbb Z}_2\oplus{\mathbb Z}_4\oplus{\mathbb Z}_5</math>
+|bgcolor=yellow|<math>{\mathbb Z}^{3}</math>
+|bgcolor=yellow|
+|
+|
+|
+|
+|- align=center
+|<math>r=18</math>
+|<math>{\mathbb Z}</math>
+|<math>{\mathbb Z}\oplus{\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}_2^{2}\oplus{\mathbb Z}_5</math>
+|bgcolor=yellow|<math>{\mathbb Z}</math>
+|
+|
+|
+|
+|- align=center
+|<math>r=19</math>
+|<math>{\mathbb Z}_2</math>
+|<math>{\mathbb Z}^{2}\oplus{\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}</math>
+|bgcolor=yellow|
+|
+|
+|
+|
+|- align=center
+|<math>r=20</math>
+|<math>{\mathbb Z}</math>
+|<math>{\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}</math>
+|bgcolor=yellow|
+|
+|
+|
+|
+|- align=center
+|<math>r=21</math>
+|<math>{\mathbb Z}_4</math>
+|<math>{\mathbb Z}</math>
+|bgcolor=yellow|
+|bgcolor=yellow|
+|
+|
+|
+|
+|- align=center
+|<math>r=22</math>
+|<math>{\mathbb Z}_2</math>
+|<math>{\mathbb Z}_2</math>
+|bgcolor=yellow|
+|bgcolor=yellow|
+|
+|
+|
+|
+|}