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A Note on Knot Floer Homology and Fixed Points of Monodromy

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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 \(\widehat{HFK}(Y,K,[F], g(F)-1)\) 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.

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Acknowledgements

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.

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  1. Department of Mathematics, Caltech, MC 253-37 1200 E California Blvd, Pasadena, CA, 91125, USA

    Yi Ni

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  1. Yi Ni
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Ni, Y. A Note on Knot Floer Homology and Fixed Points of Monodromy. Peking Math J 6, 635–643 (2023). https://doi.org/10.1007/s42543-022-00051-3

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  • DOI: https://doi.org/10.1007/s42543-022-00051-3

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