Link cobordisms and functoriality in link Floer homology

Abstract

We construct cobordism maps on link Floer homology associated to decorated link cobordisms. The maps are defined on a curved chain homotopy type invariant. We describe the construction, and prove invariance. We also make a comparison with the graph TQFT for Heegaard Floer homology.

112 pages. To appear in Journal of Topology

References in corpus (11)

• Floer homology and knot complements
• Contact structures, sutured Floer homology and TQFT
• Involutive Heegaard Floer homology
• Link cobordisms and functoriality in link Floer homology
• Connected sums and involutive knot Floer homology
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• Concordance maps in knot Floer homology
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• Tangle Floer homology and cobordisms between tangles

Cited by in corpus (18)

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• Connected sums and involutive knot Floer homology
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• Contact handles, duality, and sutured Floer homology
• Duality and mapping tori in Heegaard Floer homology
• Linear independence of rationally slice knots
• The cosmetic crossing conjecture for split links
• Tangle Floer homology and cobordisms between tangles
• A family of ${\mathfrak{sl}}_n$-like invariants in knot Floer homology
• On a Heegaard Floer theory for tangles
• Non-orientable link cobordisms and torsion order in Floer homologies
• Monopoles and Landau-Ginzburg Models I
• Locally equivalent Floer complexes and unoriented link cobordisms
• Unoriented Cobordism Maps on Link Floer Homology
• Skein relations for tangle Floer homology
• On the nonorientable four-ball genus of torus knots
• 2-torsion in instanton Floer homology
• Heegaard Floer homology and plane curves with non-cuspidal singularities