A contact invariant in sutured monopole homology

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 [1] to define a contact invariant in the instanton Floer setting.

63 pages, 28 figures; v2: material on Legendrian knots and sutured instanton homology removed and posted as separate papers

References in corpus (12)

• Heegaard Floer homologies and contact structures
• Contact structures, sutured Floer homology and TQFT
• The vanishing of the contact invariant in the presence of torsion
• Heegaard Floer invariants of Legendrian knots in contact three--manifolds
• A contact invariant in sutured monopole homology
• Instanton Floer homology and contact structures
• Sutured Floer homology and invariants of Legendrian and transverse knots
• Naturality in sutured monopole and instanton homology
• Joining and gluing sutured Floer homology
• A categorification of U_q sl(1,1) as an algebra
• The combinatorics of Morse theory with boundary
• A diagrammatic categorification of a Clifford algebra

Cited by in corpus (13)

• Khovanov homology detects the trefoils
• A contact invariant in sutured monopole homology
• Instanton Floer homology, sutures, and Heegaard diagrams
• On the equivalence of contact invariants in sutured Floer homology theories
• Contact structures, excisions, and sutured monopole Floer homology
• An enhanced Euler characteristic of sutured instanton homology
• Gluing maps and cobordism maps for sutured monopole Floer homology
• Instanton Floer homology, sutures, and Euler characteristics
• L-space knots are fibered and strongly quasipositive
• Knot surgery formulae for instanton Floer homology II: applications
• A transverse knot invariant from Z2-equivariant Heegaard Floer cohomology
• An odd analog of Plamenevskaya's invariant of transverse knots
• Knot surgery formulae for instanton Floer homology I: the main theorem