Data
:
T(9,5)/Integral Khovanov Homology
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dim
G
2
r
+
i
KH
Z
r
(
T
(
9
,
5
)
)
{\displaystyle \dim {\mathcal {G}}_{2r+i}\operatorname {KH} _{\mathbb {Z} }^{r}(T(9,5))}
i
=
19
{\displaystyle i=19}
i
=
21
{\displaystyle i=21}
i
=
23
{\displaystyle i=23}
i
=
25
{\displaystyle i=25}
i
=
27
{\displaystyle i=27}
i
=
29
{\displaystyle i=29}
i
=
31
{\displaystyle i=31}
i
=
33
{\displaystyle i=33}
r
=
0
{\displaystyle r=0}
Z
{\displaystyle {\mathbb {Z} }}
Z
{\displaystyle {\mathbb {Z} }}
r
=
1
{\displaystyle r=1}
r
=
2
{\displaystyle r=2}
Z
{\displaystyle {\mathbb {Z} }}
r
=
3
{\displaystyle r=3}
Z
2
{\displaystyle {\mathbb {Z} }_{2}}
Z
{\displaystyle {\mathbb {Z} }}
r
=
4
{\displaystyle r=4}
Z
{\displaystyle {\mathbb {Z} }}
Z
{\displaystyle {\mathbb {Z} }}
r
=
5
{\displaystyle r=5}
Z
{\displaystyle {\mathbb {Z} }}
Z
{\displaystyle {\mathbb {Z} }}
r
=
6
{\displaystyle r=6}
Z
{\displaystyle {\mathbb {Z} }}
Z
{\displaystyle {\mathbb {Z} }}
r
=
7
{\displaystyle r=7}
Z
2
{\displaystyle {\mathbb {Z} }_{2}}
Z
⊕
Z
2
{\displaystyle {\mathbb {Z} }\oplus {\mathbb {Z} }_{2}}
Z
{\displaystyle {\mathbb {Z} }}
r
=
8
{\displaystyle r=8}
Z
{\displaystyle {\mathbb {Z} }}
Z
2
{\displaystyle {\mathbb {Z} }^{2}}
r
=
9
{\displaystyle r=9}
Z
⊕
Z
2
{\displaystyle {\mathbb {Z} }\oplus {\mathbb {Z} }_{2}}
Z
2
{\displaystyle {\mathbb {Z} }^{2}}
r
=
10
{\displaystyle r=10}
Z
2
{\displaystyle {\mathbb {Z} }^{2}}
Z
2
{\displaystyle {\mathbb {Z} }_{2}}
Z
2
{\displaystyle {\mathbb {Z} }_{2}}
r
=
11
{\displaystyle r=11}
Z
2
2
⊕
Z
5
{\displaystyle {\mathbb {Z} }_{2}^{2}\oplus {\mathbb {Z} }_{5}}
Z
3
{\displaystyle {\mathbb {Z} }^{3}}
r
=
12
{\displaystyle r=12}
Z
2
{\displaystyle {\mathbb {Z} }^{2}}
Z
2
{\displaystyle {\mathbb {Z} }^{2}}
Z
2
⊕
Z
5
{\displaystyle {\mathbb {Z} }_{2}\oplus {\mathbb {Z} }_{5}}
Z
{\displaystyle {\mathbb {Z} }}
r
=
13
{\displaystyle r=13}
Z
2
{\displaystyle {\mathbb {Z} }_{2}}
Z
3
⊕
Z
2
{\displaystyle {\mathbb {Z} }^{3}\oplus {\mathbb {Z} }_{2}}
Z
2
{\displaystyle {\mathbb {Z} }^{2}}
r
=
14
{\displaystyle r=14}
Z
{\displaystyle {\mathbb {Z} }}
Z
2
{\displaystyle {\mathbb {Z} }^{2}}
Z
2
{\displaystyle {\mathbb {Z} }_{2}}
Z
{\displaystyle {\mathbb {Z} }}
r
=
15
{\displaystyle r=15}
Z
2
{\displaystyle {\mathbb {Z} }_{2}}
Z
2
⊕
Z
2
2
{\displaystyle {\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}^{2}}
Z
3
{\displaystyle {\mathbb {Z} }^{3}}
r
=
16
{\displaystyle r=16}
Z
2
{\displaystyle {\mathbb {Z} }^{2}}
Z
2
{\displaystyle {\mathbb {Z} }_{2}}
Z
⊕
Z
2
{\displaystyle {\mathbb {Z} }\oplus {\mathbb {Z} }_{2}}
Z
{\displaystyle {\mathbb {Z} }}
r
=
17
{\displaystyle r=17}
Z
2
⊕
Z
4
⊕
Z
5
{\displaystyle {\mathbb {Z} }_{2}\oplus {\mathbb {Z} }_{4}\oplus {\mathbb {Z} }_{5}}
Z
3
{\displaystyle {\mathbb {Z} }^{3}}
r
=
18
{\displaystyle r=18}
Z
{\displaystyle {\mathbb {Z} }}
Z
⊕
Z
2
{\displaystyle {\mathbb {Z} }\oplus {\mathbb {Z} }_{2}}
Z
2
2
⊕
Z
5
{\displaystyle {\mathbb {Z} }_{2}^{2}\oplus {\mathbb {Z} }_{5}}
Z
{\displaystyle {\mathbb {Z} }}
r
=
19
{\displaystyle r=19}
Z
2
{\displaystyle {\mathbb {Z} }_{2}}
Z
2
⊕
Z
2
{\displaystyle {\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}}
Z
{\displaystyle {\mathbb {Z} }}
r
=
20
{\displaystyle r=20}
Z
{\displaystyle {\mathbb {Z} }}
Z
2
{\displaystyle {\mathbb {Z} }_{2}}
Z
{\displaystyle {\mathbb {Z} }}
r
=
21
{\displaystyle r=21}
Z
4
{\displaystyle {\mathbb {Z} }_{4}}
Z
{\displaystyle {\mathbb {Z} }}
r
=
22
{\displaystyle r=22}
Z
2
{\displaystyle {\mathbb {Z} }_{2}}
Z
2
{\displaystyle {\mathbb {Z} }_{2}}
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