Categorical Chern character and braid groups

Alexei Oblomkov; Lev Rozansky

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arXiv · 1811.03257

Categorical Chern character and braid groups

Alexei Oblomkov·Lev Rozansky

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Abstract

To a braid $\beta\in Br_n$ we associate a complex of sheaves $S_\beta$ on $Hilb_n(C^2)$ such that the previously defined triply graded link homology of the closure $L(\beta)$ is isomorphic to the homology of $S_\beta$. The construction of $S_\beta$ relies on the Chern functor $CH: MF_n^{st}\to D^{per}_{C^*\times C^*}(Hilb_n(C^2))$ defined in the paper together with its adjoint functor $HC$. We prove a formula for the closure of sufficiently positive elements of the Jucys-Murphy algebra previously conjectured by Gorsky, Negut and Rasmussen.

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BibTeX RIS

Alexei Oblomkov, Lev Rozansky. 2018-11-08. Categorical Chern character and braid groups. https://arxiv.org/abs/1811.03257

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