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Unoriented Skein Exact Triangle in Link Floer Homology

A new exact triangle in low-dimensional topology showing that unoriented link Floer homology, equipped with newly defined band maps, satisfies an unoriented skein exact triangle over Z/2 for any triple of links differing inside a ball. Its proof introduces a Heegaard-Floer analogue of the 2-surgery exact triangle from instanton Floer homology, linking a knot's invariant to Heegaard Floer homology of two Dehn surgeries along it.

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AN UNORIENTED SKEIN EXACT TRIANGLE IN UNORIENTED LINK FLOER HOMOLOGY GHEEHYUN NAHM Abstract. We

Link Floer homology is a Heegaard-Floer invariant of links in a three-manifold that categorifies the Alexander polynomial; for oriented links it obeys an oriented skein exact triangle relating three …