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

Laurent Côté*, Ikshu Neithalath*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

We prove that the (τ-weighted, sheaf-theoretic) SL(2, C) Casson–Lin invariant introduced by Manolescu and the first author is generically independent of the parameter τ and additive under connected sums of knots in integral homology 3-spheres. This addresses two questions asked by Manolescu and the first author. Our arguments involve a mix of topology 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.

Original languageEnglish
JournalJournal of the Mathematical Society of Japan
Volume74
Issue number3
Pages (from-to)683-717
ISSN0025-5645
DOIs
Publication statusPublished - Jul 2022

Keywords

  • sheaf-theoretic Floer homology, Casson–Lin invariants

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