Author:
BALDWIN JOHN A.,SIVEK STEVEN
Abstract
We define an invariant of contact 3-manifolds with convex boundary using Kronheimer and Mrowka’s sutured monopole Floer homology theory ($SHM$). 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 ($SFH$). In the process of defining our invariant, we construct maps on $SHM$ associated to contact handle attachments, analogous to those defined by Honda, Kazez, and Matić in $SFH$. We use these maps to establish a bypass exact triangle in $SHM$ analogous to Honda’s in $SFH$. 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.
Publisher
Cambridge University Press (CUP)
Subject
Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis
Reference53 articles.
1. [53] R. Zarev , ‘Joining and gluing sutured Floer homology’, 2010, arXiv:1010.3496.
2. [49] Y. Tian , ‘A categorification of $U_{q}(\mathfrak{s}\mathfrak{l}(1|1))$ as an algebra’. math.QA/1210.5680, 2012.
3. [6] V. Colin , P. Ghiggini and K. Honda , ‘The equivalence of Heegaard Floer homology and embedded contact homology III: from hat to plus’. math.SG/1208.1526, 2012.
4. An Introduction to Contact Topology
5. Naturality in sutured monopole and instanton homology
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