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Gluing maps and cobordism maps in sutured monopole and instanton Floer theories

Zhenkun Li

Algebraic & Geometric Topology 21 (2021) 3019–3071
Abstract

Sutured monopole and instanton Floer homologies were introduced by Kronheimer and Mrowka (J. Differential Geom. 84 (2010) 301–364). We construct cobordism maps in these two theories and prove that such cobordism maps are functorial under the composition of cobordisms and have a duality property. Along with the construction, we also construct gluing maps in sutured monopole and instanton theories, which are of independent interest.

Keywords
balanced sutured manifolds, Floer homology, cobordisms
Mathematical Subject Classification 2010
Primary: 57M25, 57M27
References
Publication
Received: 5 February 2020
Revised: 9 August 2020
Accepted: 28 August 2020
Published: 22 November 2021
Authors
Zhenkun Li
Department of Mathematics
Stanford University
Stanford, CA
United States