# Categorical Chern character and braid groups.

@article{Oblomkov2018CategoricalCC, title={Categorical Chern character and braid groups.}, author={Alexei Oblomkov and Lev Rozansky}, journal={arXiv: Geometric Topology}, year={2018} }

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
$HC$. The properties of these functors lead us to a conjecture that $HC$ sends
$D^{per}_{C^*\times C… Expand

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