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

Li, Zhenkun

doi:10.2140/agt.2021.21.3019

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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

DOI: 10.2140/agt.2021.21.3019

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.

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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

Volume 21, issue 6 (2021)