SL(2,C) Floer cohomology for surgeries on some knots
Abstract
We establish a relationship between the sheaf-theoretic SL(2,C) Floer cohomology HP(Y), as defined by Abouzaid and Manolescu, for Y a surgery on a small knot in S^3, and the SL(2,C) Casson invariant, as defined by Curtis. We determine a similar formula involving the framed sheaf-theoretic SL(2,C) Floer cohomology, HP_#(Y). We use these relationships to compute HP and HP_# for most surgeries on two-bridge knots. We also compute HP for surgeries on two non-small knots, the granny and square knots.
Keywords
Cite
@article{arxiv.2002.04103,
title = {SL(2,C) Floer cohomology for surgeries on some knots},
author = {Ikshu Neithalath},
journal= {arXiv preprint arXiv:2002.04103},
year = {2021}
}
Comments
Revised based on referee comments on the second version. Changed the statement of Theorem 1 to be more specific. Replaced the calculations of HP for surgeries on the trefoil and figure-eight knots with a more general formula for HP and HP_# for surgery on any two-bridge knot. Accepted by Michigan Math Journal