Equivariant Floer groups for binary polyhedral spaces
type: Item
instance of: scholarly article
title: Equivariant Floer groups for binary polyhedral spaces
zbMATH Open document ID: 0821.57022
DOI: 10.1007/BF01444497
author: David M. Austin
published in: Mathematische Annalen
publication date: 1995-10-05T00:00:00Z
full work available at URL: https://eudml.org/doc/165333
review text: We compute the equivariant Floer groups for 3-manifolds \(Y_ \Gamma = S^ 3/\Gamma\) where \(\Gamma\) is a finite subgroup of \(\text{SU}(2)\). With the standard orientation induced from \(S^ 3\), we see that the equivariant Floer (co)homology generated by the irreducibles is killed off by that generated by the reducibles. This allows us to extend Donaldson's vanishing theorem for connected sums to a larger class of 4- manifolds which are split by some \(Y_ \Gamma\) with positive \(b^ +\) on both sides. A more general notion of indecomposability for algebraic surfaces results.
Mathematics Subject Classification ID: 57R57
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 778945
zbMATH Keywords: equivariant Floer groups for 3-manifolds
zbMATH Keywords: finite subgroup of \(\text{SU}(2)\)
zbMATH Keywords: Donaldson's vanishing theorem for connected sums
zbMATH Keywords: indecomposability for algebraic surfaces
MaRDI profile type: Publication
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OpenAlex ID: W2056071515
description: scientific article; zbMATH DE number 778945