Knot Floer homology and fixed points

Yi Ni

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arXiv · 2201.10546

Knot Floer homology and fixed points

Yi Ni

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Abstract

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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Yi Ni. 2022-01-25. Knot Floer homology and fixed points. https://arxiv.org/abs/2201.10546

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