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Minimal pseudo-Anosov stretch factors on nonoriented surfaces

By Livio Liechti and Balázs Strenner

Abstract

We determine the smallest stretch factor among pseudo-Anosov maps with an orientable invariant foliation on the closed nonorientable surfaces of genus 4, 5, 6, 7, 8, 10, 12, 14, 16, 18 and 20. We also determine the smallest stretch factor of an orientation-reversing pseudo-Anosov map with orientable invariant foliations on the closed orientable surfaces of genus 1, 3, 5, 7, 9 and 11. As a byproduct, we obtain that the stretch factor of a pseudo-Anosov map on a nonorientable surface or an orientation-reversing pseudo-Anosov map on an orientable surface does not have Galois conjugates on the unit circle. This shows that the techniques that were used to disprove Penner's conjecture on orientable surfaces are ineffective in the nonorientable cases.Comment: 26 pages, 6 figure

Topics: Mathematics - Geometric Topology, 57M20, 57M99, 11C08
Publisher: 'Mathematical Sciences Publishers'
Year: 2020
DOI identifier: 10.2140/agt.2020.20.451
OAI identifier: oai:arXiv.org:1806.00033

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