Pseudo-Anosov homeomorphisms of punctured non-orientable surfaces with small stretch factor
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2021
- DOI:
- 10.48550/arXiv.2107.04068
- arXiv:
- arXiv:2107.04068
- Bibcode:
- 2021arXiv210704068K
- Keywords:
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- Mathematics - Geometric Topology;
- 37E30
- E-Print:
- Accepted to Algebraic and Geometric Topology. Statement (1) on page 11 is revised, typos corrected