Volume 20, issue 5 (2020)

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Contact structures, excisions and sutured monopole Floer homology

Zhenkun Li

Algebraic & Geometric Topology 20 (2020) 2553–2588

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.

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contact structures, Floer excisions, sutured manifolds, monopole Floer homology
Mathematical Subject Classification 2010
Primary: 57M25, 57M27
Received: 14 December 2018
Revised: 4 November 2019
Accepted: 23 November 2019
Published: 4 November 2020
Zhenkun Li
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States