Data:T(8,5)/Integral Khovanov Homology: Difference between revisions

Revision as of 23:21, 26 June 2006

	$j=17$	$j=19$	$j=21$	$j=23$	$j=25$	$j=27$	$j=29$
$r=0$						${\mathbb {Z} }$	${\mathbb {Z} }$
$r=1$
$r=2$						${\mathbb {Z} }$
$r=3$						${\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=4$					${\mathbb {Z} }$	${\mathbb {Z} }$
$r=5$						${\mathbb {Z} }$	${\mathbb {Z} }$
$r=6$				${\mathbb {Z} }$	${\mathbb {Z} }$
$r=7$				${\mathbb {Z} }_{2}$	${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=8$			${\mathbb {Z} }$	${\mathbb {Z} }^{2}$
$r=9$				${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }^{2}$
$r=10$			${\mathbb {Z} }^{2}$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }_{2}$
$r=11$			${\mathbb {Z} }_{2}^{2}\oplus {\mathbb {Z} }_{5}$	${\mathbb {Z} }^{3}$
$r=12$		${\mathbb {Z} }^{2}$	${\mathbb {Z} }^{2}$	${\mathbb {Z} }_{2}\oplus {\mathbb {Z} }_{5}$	${\mathbb {Z} }$
$r=13$		${\mathbb {Z} }_{2}$	${\mathbb {Z} }^{3}\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }^{2}$
$r=14$		${\mathbb {Z} }^{2}$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=15$		${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}^{2}$	${\mathbb {Z} }^{3}$
$r=16$	${\mathbb {Z} }$	${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=17$		${\mathbb {Z} }^{2}$	${\mathbb {Z} }$
$r=18$	${\mathbb {Z} }$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }$
$r=19$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }$

@@ Line 1: / Line 1: @@
+{| border=1
-<math>t^{19} \textrm{ZMod}(0) q^{57}+t^{18} \textrm{ZMod}(0) q^{57}+t^{17} \textrm{ZMod}(0) q^{55}+t^{16} \textrm{ZMod}(0) q^{55}+t^{19} \textrm{ZMod}(2) q^{55}+t^{18} \textrm{ZMod}(2) q^{55}+t^{18} \textrm{ZMod}(0) q^{53}+t^{17} \textrm{ZMod}(0,0) q^{53}+t^{16} \textrm{ZMod}(0,2) q^{53}+t^{14} \textrm{ZMod}(0) q^{51}+t^{16} \textrm{ZMod}(0,2) q^{51}+t^{15} \textrm{ZMod}(0,0,0) q^{51}+t^{16} \textrm{ZMod}(0) q^{49}+t^{12} \textrm{ZMod}(0) q^{49}+t^{14} \textrm{ZMod}(2) q^{49}+t^{13} \textrm{ZMod}(0,0) q^{49}+t^{15} \textrm{ZMod}(0,2,2) q^{49}+t^{14} \textrm{ZMod}(0,0) q^{47}+t^{12} \textrm{ZMod}(2,5) q^{47}+t^{13} \textrm{ZMod}(0,0,0,2) q^{47}+t^{13} \textrm{ZMod}(2) q^{45}+t^{10} \textrm{ZMod}(2) q^{45}+t^{12} \textrm{ZMod}(0,0) q^{45}+t^{11} \textrm{ZMod}(0,0,0) q^{45}+t^{10} \textrm{ZMod}(2) q^{43}+t^{12} \textrm{ZMod}(0,0) q^{43}+t^9 \textrm{ZMod}(0,0) q^{43}+t^{11} \textrm{ZMod}(2,2,5) q^{43}+t^7 \textrm{ZMod}(0) q^{41}+t^{10} \textrm{ZMod}(0,0) q^{41}+t^9 \textrm{ZMod}(0,2) q^{41}+t^5 \textrm{ZMod}(0) q^{39}+t^8 \textrm{ZMod}(0,0) q^{39}+t^7 \textrm{ZMod}(0,2) q^{39}+t^8 \textrm{ZMod}(0) q^{37}+t^6 \textrm{ZMod}(0) q^{37}+t^5 \textrm{ZMod}(0) q^{37}+t^7 \textrm{ZMod}(2) q^{37}+t^6 \textrm{ZMod}(0) q^{35}+t^4 \textrm{ZMod}(0) q^{35}+t^3 \textrm{ZMod}(0) q^{35}+t^4 \textrm{ZMod}(0) q^{33}+t^3 \textrm{ZMod}(2) q^{33}+t^2 \textrm{ZMod}(0) q^{31}+\textrm{ZMod}(0) q^{29}+\textrm{ZMod}(0) q^{27}</math>
+|- align=center
+|
+|<math>j=17</math>
+|<math>j=19</math>
+|<math>j=21</math>
+|<math>j=23</math>
+|<math>j=25</math>
+|<math>j=27</math>
+|<math>j=29</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>
+|
+|bgcolor=yellow|<math>{\mathbb Z}^2</math>
+|bgcolor=yellow|<math>{\mathbb Z}_2</math>
+|<math>{\mathbb Z}</math>
+|
+|
+|
+|- align=center
+|<math>r=15</math>
+|
+|bgcolor=yellow|<math>{\mathbb Z}\oplus{\mathbb Z}_2^2</math>
+|bgcolor=yellow|<math>{\mathbb Z}^3</math>
+|
+|
+|
+|
+|- align=center
+|<math>r=16</math>
+|<math>{\mathbb Z}</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>
+|
+|
+|
+|- align=center
+|<math>r=17</math>
+|
+|bgcolor=yellow|<math>{\mathbb Z}^2</math>
+|bgcolor=yellow|<math>{\mathbb Z}</math>
+|
+|
+|
+|
+|- align=center
+|<math>r=18</math>
+|<math>{\mathbb Z}</math>
+|bgcolor=yellow|<math>{\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}</math>
+|
+|
+|
+|
+|- align=center
+|<math>r=19</math>
+|<math>{\mathbb Z}_2</math>
+|bgcolor=yellow|<math>{\mathbb Z}</math>
+|bgcolor=yellow|
+|
+|
+|
+|
+|}

Data:T(8,5)/Integral Khovanov Homology: Difference between revisions

Revision as of 23:21, 26 June 2006

Navigation menu

Page actions

Page actions

Personal tools

Navigation

Search

Tools