A construction of pseudo-Anosov homeomorphisms using positive twists

Verberne, Yvon

doi:10.2140/agt.2023.23.1601

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A construction of pseudo-Anosov homeomorphisms using positive twists

Yvon Verberne

Algebraic & Geometric Topology 23 (2023) 1601–1639

DOI: 10.2140/agt.2023.23.1601

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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Volume 23, issue 4 (2023)