Naturality in sutured monopole and instanton homology

Abstract

Kronheimer and Mrowka defined invariants of balanced sutured manifolds using monopole and instanton Floer homology. Their invariants assign isomorphism classes of modules to balanced sutured manifolds. In this paper, we introduce refinements of these invariants which assign much richer algebraic objects called projectively transitive systems of modules to balanced sutured manifolds and isomorphisms of such systems to diffeomorphisms of balanced sutured manifolds. Our work provides the foundation for extending these sutured Floer theories to other interesting functorial frameworks as well, and can be used to construct new invariants of contact structures and (perhaps) of knots and bordered 3-manifolds.

74 pages, 11 figures; v2: updated following referee's comments, added invariants of based 3-manifolds; v3: corrected definition of knot invariants, updated appendix A

References in corpus (4)

• Contact structures, sutured Floer homology and TQFT
• Instanton Floer homology and contact structures
• Joining and gluing sutured Floer homology
• Invariants of Legendrian and transverse knots in monopole knot homology

Cited by in corpus (14)

• Khovanov homology detects the trefoils
• Framed instanton homology and concordance
• A contact invariant in sutured monopole homology
• Instanton Floer homology and contact structures
• Instanton Floer homology, sutures, and Heegaard diagrams
• Stein fillings and SU(2) representations
• 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
• The cosmetic crossing conjecture for split links
• Gluing maps and cobordism maps for sutured monopole Floer homology
• Knot surgery formulae for instanton Floer homology II: applications
• 2-torsion in instanton Floer homology
• Knot surgery formulae for instanton Floer homology I: the main theorem