Categorical Chern character and braid groups

2018/11/08 by Oblomkov, Alexei, Rozansky, Lev · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1811.03257

Abstract

To a braid β∈ Br_n we associate a complex of sheaves S_β on Hilb_n(C²) such that the previously defined triply graded link homology of the closure L(β) is isomorphic to the homology of S_β. The construction of S_β relies on the Chern functor CH: MF_n^st→ D^per_{C^*× C^*}(Hilb_n(C²)) 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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