A CONTACT INVARIANT IN SUTURED MONOPOLE HOMOLOGY
Forum of Mathematics, Sigma, Tome 4 (2016)
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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.
@article{10_1017_fms_2016_11,
author = {JOHN A. BALDWIN and STEVEN SIVEK},
title = {A {CONTACT} {INVARIANT} {IN} {SUTURED} {MONOPOLE} {HOMOLOGY}},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {4},
year = {2016},
doi = {10.1017/fms.2016.11},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2016.11/}
}
JOHN A. BALDWIN; STEVEN SIVEK. A CONTACT INVARIANT IN SUTURED MONOPOLE HOMOLOGY. Forum of Mathematics, Sigma, Tome 4 (2016). doi: 10.1017/fms.2016.11
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