Connected sums and involutive knot Floer homology

Ian Zemke

doi:10.1112/plms.12227

Connected sums and involutive knot Floer homology

Ian Zemke

Mathematics

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

We prove a formula for the conjugation action on the knot Floer complex of the connected sum of two knots. Using the formula we construct a homomorphism from the smooth concordance group to an abelian group consisting of chain complexes with homotopy automorphisms, modulo an equivalence relation. Using our connected sum formula, we perform some example computations of Hendricks and Manolescu's involutive invariants on large surgeries of connected sums of knots.

Original language	English (US)
Pages (from-to)	214-265
Number of pages	52
Journal	Proceedings of the London Mathematical Society
Volume	119
Issue number	1
DOIs	https://doi.org/10.1112/plms.12227
State	Published - Jul 2019

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

57M27
57R56 (primary)

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10.1112/plms.12227

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title = "Connected sums and involutive knot Floer homology",

abstract = "We prove a formula for the conjugation action on the knot Floer complex of the connected sum of two knots. Using the formula we construct a homomorphism from the smooth concordance group to an abelian group consisting of chain complexes with homotopy automorphisms, modulo an equivalence relation. Using our connected sum formula, we perform some example computations of Hendricks and Manolescu's involutive invariants on large surgeries of connected sums of knots.",

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AB - We prove a formula for the conjugation action on the knot Floer complex of the connected sum of two knots. Using the formula we construct a homomorphism from the smooth concordance group to an abelian group consisting of chain complexes with homotopy automorphisms, modulo an equivalence relation. Using our connected sum formula, we perform some example computations of Hendricks and Manolescu's involutive invariants on large surgeries of connected sums of knots.

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Connected sums and involutive knot Floer homology

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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