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

Laurent Côté; Ikshu Neithalath

doi:10.2969/jmsj/84808480

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

Laurent Côté, Ikshu Neithalath

Harvard University

Research output: Contribution to journal › Journal article › Research › peer-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 language	English
Journal	Journal of the Mathematical Society of Japan
Volume	74
Issue number	3
Pages (from-to)	683-717
ISSN	0025-5645
DOIs	https://doi.org/10.2969/jmsj/84808480
Publication status	Published - Jul 2022

Keywords

sheaf-theoretic Floer homology, Casson–Lin invariants

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10.2969/jmsj/84808480

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

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.",

keywords = "sheaf-theoretic Floer homology, Casson–Lin invariants",

author = "Laurent C{\^o}t{\'e} and Ikshu Neithalath",

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: {\textcopyright} 2022 Mathematical Society of Japan. All rights reserved.",

year = "2022",

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doi = "10.2969/jmsj/84808480",

language = "English",

volume = "74",

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journal = "Journal of the Mathematical Society of Japan",

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TY - JOUR

T1 - On the sheaf-theoretic SL(2, C) Casson–Lin invariant

AU - Côté, Laurent

AU - Neithalath, Ikshu

N1 - 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.

PY - 2022/7

Y1 - 2022/7

N2 - 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.

AB - 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.

KW - sheaf-theoretic Floer homology, Casson–Lin invariants

U2 - 10.2969/jmsj/84808480

DO - 10.2969/jmsj/84808480

M3 - Journal article

AN - SCOPUS:85136183845

SN - 0025-5645

VL - 74

SP - 683

EP - 717

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

IS - 3

ER -

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

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