On the sheaf-theoretic SL(2,C) Casson-Lin invariant

Laurent Côté; Ikshu Neithalath

On the sheaf-theoretic SL(2,C) Casson-Lin invariant

Geometric Topology 2020-04-14 v2 Algebraic Geometry

Authors: Laurent Côté , Ikshu Neithalath

Abstract

We prove that the ( $\tau$ -weighted, sheaf-theoretic) SL(2,C) Casson-Lin invariant introduced by Manolescu and the first author in [CM19] is generically independent of the parameter $\tau$ and additive under connected sums of knots in integral homology 3-spheres. This addresses two questions asked in [CM19]. Our arguments involve a mix of topology, microlocal analysis and algebraic geometry, and rely crucially on the fact that the SL(2,C) Casson-Lin invariant admits an alternative interpretation via the theory of Behrend functions.

Keywords

casson-lin invariant sl(2,c) sheaf theory knots connected sum behrend functions

Cite

@article{arxiv.1907.02593,
  title  = {On the sheaf-theoretic SL(2,C) Casson-Lin invariant},
  author = {Laurent Côté and Ikshu Neithalath},
  journal= {arXiv preprint arXiv:1907.02593},
  year   = {2020}
}

Comments

29 pages; v2: minor modifications and expanded introduction

On the sheaf-theoretic SL(2,C) Casson-Lin invariant

Abstract

Keywords

Cite

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