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Unoriented Cobordism Maps on Link Floer Homology

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arxiv 1711.07110 v2 pith:YFEEGYTJ submitted 2017-11-20 math.GT

Haofei Fan This is my paper · ORCID
classification math.GT
keywords linkcobordismunorientedfloerhomologymapsdisorientedindex
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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 Oszv\'ath-Stipsicz-Szab\'o's and Manolescu's constructions of link cobordism maps for an unoriented band move.

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Cited by 1 Pith paper

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  1. An unoriented skein exact triangle in unoriented link Floer homology

    math.GT 2025-01 conditional novelty 8.0 of 10

    Unoriented link Floer homology satisfies an unoriented skein exact triangle over Z/2, with band maps matching Khovanov homology for planar links.

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