APPLICATIONS of INVOLUTIVE HEEGAARD FLOER HOMOLOGY

Kristen Hendricks; Jennifer Hom; Tye Lidman

doi:10.1017/S147474801900015X

APPLICATIONS of INVOLUTIVE HEEGAARD FLOER HOMOLOGY

Kristen Hendricks, Jennifer Hom, Tye Lidman

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

15 Scopus citations

Abstract

We use Heegaard Floer homology to define an invariant of homology cobordism. This invariant is isomorphic to a summand of the reduced Heegaard Floer homology of a rational homology sphere equipped with a spin structure and is analogous to Stoffregen's connected Seiberg-Witten Floer homology. We use this invariant to study the structure of the homology cobordism group and, along the way, compute the involutive correction terms and for certain families of three-manifolds.

Original language	English (US)
Pages (from-to)	187-224
Number of pages	38
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	20
Issue number	1
DOIs	https://doi.org/10.1017/S147474801900015X
State	Published - Jan 2021
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

2010 Mathematics subject classification 57M27 57M58

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10.1017/S147474801900015X

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abstract = "We use Heegaard Floer homology to define an invariant of homology cobordism. This invariant is isomorphic to a summand of the reduced Heegaard Floer homology of a rational homology sphere equipped with a spin structure and is analogous to Stoffregen's connected Seiberg-Witten Floer homology. We use this invariant to study the structure of the homology cobordism group and, along the way, compute the involutive correction terms and for certain families of three-manifolds.",

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AU - Hom, Jennifer

AU - Lidman, Tye

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AB - We use Heegaard Floer homology to define an invariant of homology cobordism. This invariant is isomorphic to a summand of the reduced Heegaard Floer homology of a rational homology sphere equipped with a spin structure and is analogous to Stoffregen's connected Seiberg-Witten Floer homology. We use this invariant to study the structure of the homology cobordism group and, along the way, compute the involutive correction terms and for certain families of three-manifolds.

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APPLICATIONS of INVOLUTIVE HEEGAARD FLOER HOMOLOGY

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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