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Pseudo-Anosov homeomorphisms of punctured nonorientable surfaces with small stretch factor

Sayantan Khan, Caleb Partin and Rebecca R Winarski

Algebraic & Geometric Topology 23 (2023) 2823–2856
Abstract

We prove that in the nonorientable setting, the minimal stretch factor of a pseudo-Anosov homeomorphism of a surface of genus g with a fixed number of punctures is asymptotically on the order of 1g. Our result adapts the work of Yazdi to nonorientable surfaces. We include the details of Thurston’s theory of fibered faces for nonorientable 3–manifolds.

Keywords
mapping class group, pseudo-Anosov, nonorientable surfaces, minimal stretch factor
Mathematical Subject Classification
Primary: 37E30
References
Publication
Received: 20 July 2021
Revised: 25 October 2021
Accepted: 7 December 2021
Published: 7 September 2023
Authors
Sayantan Khan
Department of Mathematics
University of Michigan
Ann Arbor, MI
United States
https://www-personal.umich.edu/~saykhan/
Caleb Partin
School of Mathematics
Georgia Institute of Technology
Atlanta, GA
United States
Rebecca R Winarski
Department of Mathematics and Computer Science
College of the Holy Cross
Worcester, MA
United States
https://sites.google.com/site/rebeccawinarski/

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