Geodesics in the mapping class group
arXiv:1810.12489 · doi:10.2140/agt.2021.21.2995
Abstract
We construct explicit examples of geodesics in the mapping class group and show that the shadow of a geodesic in mapping class group to the curve graph does not have to be a quasi-geodesic. We also show that the quasi-axis of a pseudo-Anosov element of the mapping class group may not have the strong contractibility property. Specifically, we show that, after choosing a generating set carefully, one can find a pseudo-Anosov homeomorphism f, a sequence of points w_k and a sequence of radii r_k so that the ball B(w_k, r_k) is disjoint from a quasi-axis a of f, but for any projection map from mapping class group to a, the diameter of the image of B(w_k, r_k) grows like log(r_k).
arXiv comment16 pages, 3 figures
References in corpus (8)
- Geometry of the Complex of Curves I: Hyperbolicity
- Asymptotic geometry of the mapping class group and Teichmueller space
- Uniform hyperbolicity of the curve graph via surgery sequences
- Bounded geometry for Kleinian groups
- Growth Tight Actions
- Large scale rank of Teichmuller space
- The shadow of a Thurston geodesic to the curve graph
- Genericity of contracting elements in groups