Contact structures, sutured Floer homology and TQFT

Abstract

We describe the natural gluing map on sutured Floer homology which is induced by the inclusion of one sutured manifold (M',Γ') into a larger sutured manifold (M,Γ), together with a contact structure on M-M'. As an application of this gluing map, we produce a (1+1)-dimensional TQFT by dimensional reduction and study its properties.

37 pages, 19 figures

References in corpus (7)

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• On the classification of tight contact structures I
• Floer homology and surface decompositions
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• The vanishing of the contact invariant in the presence of torsion
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Cited by in corpus (35)

• Cobordisms of sutured manifolds and the functoriality of link Floer homology
• Khovanov homology detects the trefoils
• Link cobordisms and functoriality in link Floer homology
• Bordered Floer homology for sutured manifolds
• Sutures and contact homology I
• The equivalence of Heegaard Floer homology and embedded contact homology III: from hat to plus
• A Hierarchy of Local Symplectic Filling Obstructions for Contact 3-Manifolds
• Connected sums and involutive knot Floer homology
• A contact invariant in sutured monopole homology
• Knot cobordisms, bridge index, and torsion in Floer homology
• Giroux torsion and twisted coefficients
• Sutured Floer homology and invariants of Legendrian and transverse knots
• On the Frøyshov invariant and monopole Lefschetz number
• Instanton Floer homology, sutures, and Heegaard diagrams
• Naturality in sutured monopole and instanton homology
• Joining and gluing sutured Floer homology
• Contact handles, duality, and sutured Floer homology
• On symplectic fillings of spinal open book decompositions I: Geometric constructions
• A categorification of U_T sl(1,1) and its tensor product representations
• Conifold transitions via affine geometry and mirror symmetry
• Itsy bitsy topological field theory
• On the transverse invariant for bindings of open books
• An enhanced Euler characteristic of sutured instanton homology
• Gluing maps and cobordism maps for sutured monopole Floer homology
• Infinitely many universally tight torsion free contact structures with vanishing Ozsváth-Szabó contact invariants
• Dimensionally-reduced sutured Floer homology as a string homology
• On symplectic fillings of spinal open book decompositions II: Holomorphic curves and classification
• Tight contact structures on Seifert surface complements
• A friendly introduction to the bordered contact invariant
• On invariants for Legendrian knots
• Combinatorial Sutured TQFT as Exterior Algebra
• On contact surgery and knot Floer invariants
• Introduction to sutured Floer homology
• An exposition of the equivalence of Heegaard Floer homology and embedded contact homology
• Foliations, contact structures and their interactions in dimension three