Unoriented Cobordism Maps on Link Floer Homology

Haofei Fan (UCLA)

We study the problem of defining maps on link Floer homology induced by unoriented link cobordisms. We provide a natural notion of link cobordism, bipartite disoriented link cobordism, which tracks not only the motion of the basepoints of the link but also the motion of index zero and index three critical points. Then we construct a map on unoriented link Floer homology associated to a bipartite 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.