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

From Knot Atlas
Jump to navigationJump to search
No edit summary
 
No edit summary
Line 1: Line 1:
{| border=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>j=19</math>
|<math>j=21</math>
|<math>j=23</math>
|<math>j=25</math>
|<math>j=27</math>
|<math>j=29</math>
|<math>j=31</math>
|<math>j=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|
|
|
|
|
|}

Revision as of 23:21, 26 June 2006

[math]\displaystyle{ j=19 }[/math] [math]\displaystyle{ j=21 }[/math] [math]\displaystyle{ j=23 }[/math] [math]\displaystyle{ j=25 }[/math] [math]\displaystyle{ j=27 }[/math] [math]\displaystyle{ j=29 }[/math] [math]\displaystyle{ j=31 }[/math] [math]\displaystyle{ j=33 }[/math]
[math]\displaystyle{ r=0 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=1 }[/math]
[math]\displaystyle{ r=2 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=3 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=4 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=5 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=6 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=7 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}\oplus{\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=8 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math] [math]\displaystyle{ {\mathbb Z}^2 }[/math]
[math]\displaystyle{ r=9 }[/math] [math]\displaystyle{ {\mathbb Z}\oplus{\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}^2 }[/math]
[math]\displaystyle{ r=10 }[/math] [math]\displaystyle{ {\mathbb Z}^2 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math]
[math]\displaystyle{ r=11 }[/math] [math]\displaystyle{ {\mathbb Z}_2^2\oplus{\mathbb Z}_5 }[/math] [math]\displaystyle{ {\mathbb Z}^3 }[/math]
[math]\displaystyle{ r=12 }[/math] [math]\displaystyle{ {\mathbb Z}^2 }[/math] [math]\displaystyle{ {\mathbb Z}^2 }[/math] [math]\displaystyle{ {\mathbb Z}_2\oplus{\mathbb Z}_5 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=13 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}^3\oplus{\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}^2 }[/math]
[math]\displaystyle{ r=14 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math] [math]\displaystyle{ {\mathbb Z}^2 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=15 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}^2\oplus{\mathbb Z}_2^2 }[/math] [math]\displaystyle{ {\mathbb Z}^3 }[/math]
[math]\displaystyle{ r=16 }[/math] [math]\displaystyle{ {\mathbb Z}^2 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}\oplus{\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=17 }[/math] [math]\displaystyle{ {\mathbb Z}_2\oplus{\mathbb Z}_4\oplus{\mathbb Z}_5 }[/math] [math]\displaystyle{ {\mathbb Z}^3 }[/math]
[math]\displaystyle{ r=18 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math] [math]\displaystyle{ {\mathbb Z}\oplus{\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}_2^2\oplus{\mathbb Z}_5 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=19 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}^2\oplus{\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=20 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=21 }[/math] [math]\displaystyle{ {\mathbb Z}_4 }[/math] [math]\displaystyle{ {\mathbb Z} }[/math]
[math]\displaystyle{ r=22 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math] [math]\displaystyle{ {\mathbb Z}_2 }[/math]
Retrieved from "https://katlas.org/index.php?title=Data:T(9,5)/Integral_Khovanov_Homology&oldid=50609"