On fixed points of pseudo-Anosov maps

Tarik Aougab; David Futer; Samuel J. Taylor

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arXiv · 2509.07818

On fixed points of pseudo-Anosov maps

Tarik Aougab·David Futer·Samuel J. Taylor

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Abstract

We give a formula to estimate the number of fixed points of a pseudo-Anosov homeomorphism of a surface. When the homeomorphism satisfies a mild property called strong irreducibility, the log of the number of fixed points is coarsely equal to the Teichmuller translation length. We also discuss several applications, including an inequality relating the hyperbolic volume of a mapping torus to the rank of its Heegaard Floer homology.

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Tarik Aougab, David Futer, Samuel J. Taylor. 2025-09-09. On fixed points of pseudo-Anosov maps. https://arxiv.org/abs/2509.07818

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