Floer homology of connected sum of homology 3-spheres
type: Item
instance of: scholarly article
title: Floer homology of connected sum of homology 3-spheres
zbMATH Open document ID: 0848.58010
DOI: 10.1016/0040-9383(95)00009-7
author: Kenji Fukaya
published in: Topology
publication date: 1996-11-04T00:00:00Z
review text: Let \(M\) be a homology 3-sphere. Then the space \(R(M)\) consisting of the conjugacy classes of SU(2) representations of the fundamental group \(\pi_1(M)\) can be identified with the set of critical points of the Chern-Simons functional on an infinite-dimensional space of gauge equivalence classes of connections on \(M\). The author studies the Floer homology group \(I_*(M)\) [\textit{A. Floer}, Commun. Math. Phys. 118, No. 2, 215-240 (1988; Zbl 0684.53027)] in the case when \(R(M)\) is of positive dimension. There is a generalization of Morse theory by Bott to the case when the critical point set is a nondegenerate smooth manifold. In the first part of the paper the author is concerned with an infinite-dimensional version of this case. In the second part the results are applied to the case when \(M\) is a connected sum of two homology spheres. The existence of a spectral sequence and some long exact sequence are established.
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 55N35
Mathematics Subject Classification ID: 53C07
zbMATH DE Number: 863696
zbMATH Keywords: Floer homology
zbMATH Keywords: critical manifolds
zbMATH Keywords: homology 3-spheres
reviewed by: Vitaly Moroz
MaRDI profile type: Publication
full work available at URL: 0040-9383(95)00009-7
OpenAlex ID: W1990303340
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description: scientific article; zbMATH DE number 863696