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

DOI10.2969/JMSJ/84808480arXiv1907.02593MaRDI QIDQ6321553

Laurent Côté, Ikshu Neithalath

Publication date: 4 July 2019

Abstract: We prove that the ($au$-weighted, sheaf-theoretic) SL(2,C) Casson-Lin invariant introduced by Manolescu and the first author in [CM19] is generically independent of the parameter $au$ 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.

Mathematics Subject Classification ID

Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) (32S60) Knot theory (57K10) Homology theories in knot theory (Khovanov, Heegaard-Floer, etc.) (57K18)

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