2. KhovanovRozansky homology

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 $HH(\beta):=\text{Ext}_{R\text{ bimod}}(R,B)$. 
Problem 2.3.
Compute the KhovanovRozansky homology $HHH$ of cables of torus knots and develop a recursion for this class of knots. 
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.
Remark. Pavel Galashin suggests there may be a relation to convexity.

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