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

Laurent Côté, Ikshu Neithalath

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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.

TidsskriftJournal of the Mathematical Society of Japan
Udgave nummer3
Sider (fra-til)683-717
StatusUdgivet - jul. 2022

Bibliografisk note

Funding Information:
2020 Mathematics Subject Classification. Primary 57K10; Secondary 32S60, 57K18. Key Words and Phrases. sheaf-theoretic Floer homology, Casson–Lin invariants. The first author was supported by a Stanford University Benchmark Graduate Fellowship.

Publisher Copyright:
© 2022 Mathematical Society of Japan. All rights reserved.


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