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Results tagged with khovanov-homology
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user 17644
Khovanov homology, constructed by Mikhail Khovanov, is a categorification of the Jones polynomial.
2
votes
0
answers
131
views
Unnormalized Kauffman homology of the unknot
Is the unnormalized Kauffman homology of the unknot known? The Poincare polynomial of HOMFLY homology of the unknot is known as
$$\frac{1+at}{1-q}.$$
Is the Poincare polynomials of Kauffman homology …
- 2,273
4
votes
1
answer
375
views
Khovanov $sl_2$ homology of a connected sum of some torus knots
Let $T_{p,q}$ be the (p,q) torus knot. Could anybody possibly compute either unreduced or reduced Khovanov $\mathfrak{sl}(2)$ homology of the connected sum $T_{2,3} \sharp T_{3,4}$ of the (2,3) and (3 …
- 2,273
0
votes
Khovanov-Rozansky homology and spectral sequences
In the paper by Gukov and Stosic, they formulate the axioms which colored HOMFLY homology (triply-graded homology) is supposed to satisfy, assuming there exists such homology. If you apply the $d_M$ d …
- 2,273
7
votes
0
answers
412
views
Khovanov homology and Crane-Yetter TQFT
Crane-Yetter(-Kauffman) have constructed 4-dimensional TQFT in such a way that Reshetikhin-Turaev theory lives on the boundary $\partial M$ of a 4-manifold $M$. Therefore, Crane-Yetter TQFT can be tho …
- 2,273
1
vote
0
answers
224
views
Categorification of WRT invariants of integral homology spheres
First, I would like to know how many definitions are there for categorification of WRT invariants. In addition, I wonder if the categorified version of WRT invariants have been explicitly computed for …
- 2,273