Pseudo-Anosov homeomorphisms of punctured non-orientable surfaces with small stretch factor

We prove that in the non-orientable 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 \(\frac{1}{g}\). Our result adapts the work of Yazdi to non-orientable surfaces. We include the deta...

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Bibliographic Details
Published in:arXiv.org 2021-12
Main Authors: Khan, Sayantan, Partin, Caleb, Winarski, Rebecca R
Format: Article
Language:English
Online Access:Get full text
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Summary:We prove that in the non-orientable 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 \(\frac{1}{g}\). Our result adapts the work of Yazdi to non-orientable surfaces. We include the details of Thurston's theory of fibered faces for non-orientable 3-manifolds.
ISSN:2331-8422
DOI:10.48550/arxiv.2107.04068