Geodesics in the mapping class group
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Publication:6308957
DOI10.2140/AGT.2021.21.2995arXiv1810.12489MaRDI QIDQ6308957
Publication date: 29 October 2018
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).
Topological methods in group theory (57M07) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34)
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