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$\mathrm{HF}=\mathrm{HM}$, III: Holomorphic curves and the differential for the ech/Heegaard Floer correspondence

Çağatay Kutluhan, Yi-Jen Lee and Clifford Henry Taubes

Geometry & Topology 24 (2020) 3013–3218
DOI: 10.2140/gt.2020.24.3013
Abstract

This is the third of five papers that construct an isomorphism between the Seiberg–Witten Floer homology and the Heegaard Floer homology of a given compact, oriented 3–manifold. The isomorphism is given as a composition of three isomorphisms; the first of these relates a version of embedded contact homology on an auxiliary manifold to the Heegaard Floer homology on the original. This paper describes the relationship between the differential on the embedded contact homology chain complex and the differential on the Heegaard Floer chain complex. The paper also describes the relationship between the various canonical endomorphisms that act on the homology groups of these two complexes.

Keywords
Seiberg–Witten Floer homology, Heegaard Floer homology
Mathematical Subject Classification 2010
Primary: 53D42
References
Publication
Received: 17 February 2012
Revised: 14 September 2016
Accepted: 23 April 2018
Published: 29 December 2020
Proposed: Tomasz Mrowka
Seconded: András I Stipsicz, Bruce Kleiner
Authors
Çağatay Kutluhan
Department of Mathematics
University at Buffalo
Buffalo, NY
United States
Yi-Jen Lee
Institute of Mathematical Sciences
The Chinese University of Hong Kong
Shatin, NT
Hong Kong
Clifford Henry Taubes
Department of Mathematics
Harvard University
Cambridge, MA
United States