The authors compute the E2 page of the Rasmussen spectral sequence for stable gl_N Khovanov-Rozansky homology of torus knots, verifying the predicted algebraic description for all N.
An Algebra Structure for the stable Khovanov homology of torus links
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abstract
The family of negative torus links $T_{p,q}$ over a fixed number of strands $p$ admits a stable limit in reduced Khovanov homology as $q$ grows to infinity. In this paper, we endow this stable space with a bi-graded commutative algebra structure. We describe these algebras explicitly for $p=2,3,4$. As an application, we compute the homology of two families of links, and produce a lower bound for the width of the homology of any $4$-stranded torus link.
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Stable deformed $\mathfrak{gl}_N$ homology of torus knots
The authors compute the E2 page of the Rasmussen spectral sequence for stable gl_N Khovanov-Rozansky homology of torus knots, verifying the predicted algebraic description for all N.