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A construction of pseudo-Anosov homeomorphisms using positive twists

Yvon Verberne

Algebraic & Geometric Topology 23 (2023) 1601–1639
Abstract

We introduce a construction of pseudo-Anosov homeomorphisms on n–times punctured spheres and surfaces of higher genus using only positive half-twists and Dehn twists. These constructions produce explicit examples of pseudo-Anosov maps with various number-theoretic properties associated to the stretch factors. For instance, we produce examples where the trace field is not totally real and the Galois conjugates of the stretch factor are on the unit circle. It follows that for these examples, no power of these maps can arise from either Thurston’s or Penner’s constructions.

Keywords
mapping class group, pseudo-Anosov homeomorphisms
Mathematical Subject Classification 2010
Primary: 15A18, 37E30, 57M07
References
Publication
Received: 8 August 2019
Revised: 23 September 2021
Accepted: 11 October 2021
Published: 14 June 2023
Authors
Yvon Verberne
School of Mathematics
Georgia Institute of Technology
Atlanta, GA
United States
https://sites.google.com/view/yvonverberne

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