Work

On fixed points of pseudo-Anosov maps

Year: 2026

Type: article

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 Teichmüller 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.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1821

Authors: Tarik Aougab, David Futer, Samuel J. Taylor

Institutions: Haverford College, Temple University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Awards: Hyperbolic manifolds and groups, Topology and Geometry from 3-Manifolds to Free Groups, Beyond fibrations: flows, foliations, and geometry from 3-manifolds to free-by-cyclic groups