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Published October 12, 2022 | public
Journal Article

A Note on Knot Floer Homology and Fixed Points of Monodromy

Ni, Yi ORCID icon

Abstract

Using an argument of Baldwin–Hu–Sivek, we prove that if K is a hyperbolic fibered knot with fiber F in a closed, oriented 3-manifold Y, and HFKˆ(Y,K,[F],g(F)−1) has rank 1, then the monodromy of K is freely isotopic to a pseudo-Anosov map with no fixed points. In particular, this shows that the monodromy of a hyperbolic L-space knot is freely isotopic to a map with no fixed points.

Additional Information

The author was partially supported by NSF Grant Number DMS-1811900. The author wishes to thank John Baldwin for many helpful discussions and comments on a draft of this paper.

Additional details

Created:
August 22, 2023
Modified:
October 24, 2023