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.

Accepted to Algebraic and Geometric Topology. Statement (1) on page 11 is revised, typos corrected

References in corpus (1)

• A family of pseudo-Anosov braids with small dilatation

Cited by in corpus (2)

• The Klein bottle has stably unbounded homeomorphism group
• Fibered 3-manifolds and Veech groups