A contact invariant in sutured monopole homology

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Title: A contact invariant in sutured monopole homology
Author(s): Baldwin, JA
Sivek, S
Item Type: Journal Article
Abstract: We define an invariant of contact 3-manifolds with convex boundary using Kronheimer and Mrowka’s sutured monopole Floer homology theory ( ). Our invariant can be viewed as a generalization of Kronheimer and Mrowka’s contact invariant for closed contact 3-manifolds and as the monopole Floer analogue of Honda, Kazez, and Matić’s contact invariant in sutured Heegaard Floer homology ( ). In the process of defining our invariant, we construct maps on associated to contact handle attachments, analogous to those defined by Honda, Kazez, and Matić in . We use these maps to establish a bypass exact triangle in analogous to Honda’s in . This paper also provides the topological basis for the construction of similar gluing maps in sutured instanton Floer homology, which are used in Baldwin and Sivek [Selecta Math. (N.S.), 22(2) (2016), 939–978] to define a contact invariant in the instanton Floer setting.
Publication Date: 10-Jun-2016
Date of Acceptance: 14-May-2016
URI: http://hdl.handle.net/10044/1/50329
DOI: https://dx.doi.org/10.1017/fms.2016.11
ISSN: 2050-5094
Publisher: Cambridge University Press (CUP)
Journal / Book Title: Forum of Mathematics, Sigma
Volume: 4
Copyright Statement: © The Author(s) 2016 This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Keywords: math.SG
Publication Status: Published
Article Number: e12
Open Access location: https://www.cambridge.org/core/journals/forum-of-mathematics-sigma/article/contact-invariant-in-sutured-monopole-homology/6F7FC3250E8596AA96EB81C735A4037F
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