PIN(2)-monopole Floer homology and the Rokhlin invariant

Francesco Lin

doi:10.1112/S0010437X18007510

PIN(2)-monopole Floer homology and the Rokhlin invariant

Francesco Lin

Mathematics

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

2 Scopus citations

Abstract

We show that the bar version of the -monopole Floer homology of a three-manifold equipped with a self-conjugate spin structure is determined by the triple cup product of together with the Rokhlin invariants of the spin structures inducing . This is a manifestation of mod index theory and can be interpreted as a three-dimensional counterpart of Atiyah's classical results regarding spin structures on Riemann surfaces.

Original language	English (US)
Pages (from-to)	2681-2700
Number of pages	20
Journal	Compositio Mathematica
Volume	154
Issue number	12
DOIs	https://doi.org/10.1112/S0010437X18007510
State	Published - Dec 1 2018

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Keywords

Rokhlin invariant
monopole Floer homology
quaternionic operators

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10.1112/S0010437X18007510

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abstract = "We show that the bar version of the -monopole Floer homology of a three-manifold equipped with a self-conjugate spin structure is determined by the triple cup product of together with the Rokhlin invariants of the spin structures inducing . This is a manifestation of mod index theory and can be interpreted as a three-dimensional counterpart of Atiyah's classical results regarding spin structures on Riemann surfaces.",

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author = "Francesco Lin",

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N1 - Publisher Copyright: © The Author 2018.

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N2 - We show that the bar version of the -monopole Floer homology of a three-manifold equipped with a self-conjugate spin structure is determined by the triple cup product of together with the Rokhlin invariants of the spin structures inducing . This is a manifestation of mod index theory and can be interpreted as a three-dimensional counterpart of Atiyah's classical results regarding spin structures on Riemann surfaces.

AB - We show that the bar version of the -monopole Floer homology of a three-manifold equipped with a self-conjugate spin structure is determined by the triple cup product of together with the Rokhlin invariants of the spin structures inducing . This is a manifestation of mod index theory and can be interpreted as a three-dimensional counterpart of Atiyah's classical results regarding spin structures on Riemann surfaces.

KW - Rokhlin invariant

KW - monopole Floer homology

KW - quaternionic operators

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JO - Compositio Mathematica

JF - Compositio Mathematica

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ER -

PIN(2)-monopole Floer homology and the Rokhlin invariant

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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