Geodesic length spectrum of hyperelliptic connected components

Corentin Boissy (1) , Erwan Lanneau (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IF - Institut Fourier

We propose a general framework for studying pseudo-Anosov homeomorphisms on translation surfaces. This new approach, among other consequences, allows us to compute the systole of the Teichmueller geodesic flow restricted to the hyperelliptic connected components, settling a question of Farb. We stress that all proofs and computations are performed without the help of a computer. As a byproduct, our methods give a way to describe the bottom of the lengths spectrum of the hyperelliptic components.

Domaines: Topologie géométrique [math.GT]

Corentin Boissy, Erwan Lanneau. Geodesic length spectrum of hyperelliptic connected components. 2018. ⟨hal-01962229⟩