Knot Floer homology and fixed points

2022/01/25 by Ni, Yi · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2201.10546

Abstract

If K is a fibered knot in a closed, oriented 3--manifold Y with fiber F, and \widehatHFK(Y,K,[F], g(F)-1;\mathbb Z/2\mathbb Z) has rank r, then the monodromy of K is freely isotopic to a diffeomorphism with at most r-1 fixed points. This generalizes earlier work of Baldwin--Hu--Sivek and Ni. We also clarify a misleading formula in Cotton-Clay's computation of the symplectic Floer homology of mapping classes of surfaces.

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