Colored Khovanov-Rozansky homology for infinite braids
Abstract
We show that the limiting unicolored Khovanov-Rozansky chain complex of any infinite positive braid categorifies a highest-weight projector. This result extends an earlier result of Cautis categorifying highest-weight projectors using the limiting complex of infinite torus braids. Additionally, we show that the results hold in the case of colored HOMFLY-PT Khovanov-Rozansky homology as well. An application of this result is given in finding a partial isomorphism between the HOMFLY-PT homology of any braid positive link and the stable HOMFLY-PT homology of the infinite torus knot as computed by Hogancamp.
Keywords
Cite
@article{arxiv.1709.06666,
title = {Colored Khovanov-Rozansky homology for infinite braids},
author = {Michael Abel and Michael Willis},
journal= {arXiv preprint arXiv:1709.06666},
year = {2019}
}
Comments
30 pages, many figures. This new version (Oct 24, 2019) contains several small corrections and clarifications (thanks to the referee for pointing many of these out)