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2. Khovanov-Rozansky homology


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      Problem 2.1.

      Is the Khovanov-Rozansky homology functorial?


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          Problem 2.2.

          If $w^2=1$, we have a map $B_w\rightarrow R$. Is the induced map $HH(B_w)\rightarrow HH(R)$ injective? Given that the Hochschild homology is defined as $HH(\beta):=\text{Ext}_{R-\text{ bimod}}(R,B)$.


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              Problem 2.3.

              Compute the Khovanov-Rozansky homology $HHH$ of cables of torus knots and develop a recursion for this class of knots.


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                  Problem 2.4.

                  Compute $HHH(JM_1^{t_1}\dots JM_n^{t_n})$ "for as many $t$’s as possible" is it parity? Describe it as an $R$-module.
                    1. Remark. Pavel Galashin suggests there may be a relation to convexity.


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                          Problem 2.5.

                          Describe annulus maps in Khovanov-Rozansky homology $HHH$.

                              Cite this as: AimPL: Algebra, geometry, and combinatorics of link homology, available at http://aimpl.org/agclinkhom.