Unoriented Cobordism Maps on Link Floer Homology

Abstract

We study the problem of defining maps on link Floer homology induced by unoriented link cobordisms. We provide a natural notion of link cobordism, disoriented link cobordism, which tracks the motion of index zero and index three critical points. Then we construct a map on unoriented link Floer homology associated to a disoriented link cobordism. Furthermore, we give a comparison with Oszváth-Stipsicz-Szabó's and Manolescu's constructions of link cobordism maps for an unoriented band move.

Major revision: We now work with disoriented link cobordisms inside cylinders

References in corpus (4)

• Concordance homomorphisms from knot Floer homology
• Link cobordisms and functoriality in link Floer homology
• Defining and classifying TQFTs via surgery
• An involutive upsilon knot invariant

Cited by in corpus (1)

• Tangle Floer homology and cobordisms between tangles