A connected sum formula for involutive Heegaard Floer homology

Kristen Hendricks; Ciprian Manolescu; Ian Zemke

doi:10.1007/s00029-017-0332-8

A connected sum formula for involutive Heegaard Floer homology

Kristen Hendricks, Ciprian Manolescu, Ian Zemke

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

27 Scopus citations

Abstract

We prove a connected sum formula for involutive Heegaard Floer homology, and use it to study the involutive correction terms of connected sums. In particular, we give an example of a three-manifold with d̲(Y)≠d(Y)≠d¯(Y). We also construct a homomorphism from the three-dimensional homology cobordism group to an algebraically defined Abelian group, consisting of certain complexes (equipped with a homotopy involution) modulo a notion of local equivalence.

Original language	English (US)
Pages (from-to)	1183-1245
Number of pages	63
Journal	Selecta Mathematica, New Series
Volume	24
Issue number	2
DOIs	https://doi.org/10.1007/s00029-017-0332-8
State	Published - Apr 1 2018
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Physics and Astronomy
General Mathematics

Keywords

57M27 (Secondary)
57R58 (Primary)

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10.1007/s00029-017-0332-8

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AU - Manolescu, Ciprian

AU - Zemke, Ian

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N2 - We prove a connected sum formula for involutive Heegaard Floer homology, and use it to study the involutive correction terms of connected sums. In particular, we give an example of a three-manifold with d̲(Y)≠d(Y)≠d¯(Y). We also construct a homomorphism from the three-dimensional homology cobordism group to an algebraically defined Abelian group, consisting of certain complexes (equipped with a homotopy involution) modulo a notion of local equivalence.

AB - We prove a connected sum formula for involutive Heegaard Floer homology, and use it to study the involutive correction terms of connected sums. In particular, we give an example of a three-manifold with d̲(Y)≠d(Y)≠d¯(Y). We also construct a homomorphism from the three-dimensional homology cobordism group to an algebraically defined Abelian group, consisting of certain complexes (equipped with a homotopy involution) modulo a notion of local equivalence.

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KW - 57R58 (Primary)

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A connected sum formula for involutive Heegaard Floer homology

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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