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arxiv: 2201.10546 · v2 · submitted 2022-01-25 · 🧮 math.GT · math.SG

Knot Floer homology and fixed points

Yi Ni This is my paper
classification 🧮 math.GT math.SG
keywords fixedfloerhomologyknotmathbbpointsbaldwin--hu--sivekclarify
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If $K$ is a fibered knot in a closed, oriented $3$--manifold $Y$ with fiber $F$, and $\widehat{HFK}(Y,K,[F], g(F)-1;\mathbb Z/2\mathbb Z)$ 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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    Authors supply an estimate for fixed points of pseudo-Anosov maps and prove that, under strong irreducibility, log of the count is coarsely the Teichmuller length, plus volume-homology inequalities for mapping tori.