Contact structures, excisions and sutured monopole Floer homology

Li, Zhenkun

doi:10.2140/agt.2020.20.2553

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Contact structures, excisions and sutured monopole Floer homology

Zhenkun Li

Algebraic & Geometric Topology 20 (2020) 2553–2588

DOI: 10.2140/agt.2020.20.2553

Abstract

We explore the interplay between contact structures and sutured monopole Floer homology. First, we study the behavior of contact elements, which were defined by Baldwin and Sivek, under the operation of performing Floer excisions, which was introduced to the context of sutured monopole Floer homology by Kronheimer and Mrowka. We then compute the sutured monopole Floer homology of some special balanced sutured manifolds, using tools closely related to contact geometry. For an application, we obtain an exact triangle for the oriented skein relation in monopole theory and derive a connected sum formula for sutured monopole Floer homology.

Keywords

contact structures, Floer excisions, sutured manifolds, monopole Floer homology

Mathematical Subject Classification 2010

Primary: 57M25, 57M27

References

Publication

Received: 14 December 2018

Revised: 4 November 2019

Accepted: 23 November 2019

Published: 4 November 2020

Authors

Zhenkun Li
Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States

Volume 20, issue 5 (2020)