The action of the mapping class group on the space of geodesic rays of a punctured hyperbolic surface
Brian H. Bowditch
University of Warwick, Coventry, UKMakoto Sakuma
Hiroshima University, Higashi-Hiroshima, Japan
![The action of the mapping class group on the space of geodesic rays of a punctured hyperbolic surface cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-ggd-volume-12-issue-2.png&w=3840&q=90)
Abstract
Let be a complete finite-area orientable hyperbolic surface with one cusp, and let be the space of complete geodesic rays in emanating from the puncture. Then there is a natural action of the mapping class group of on . We show that this action is "almost everywhere" wandering.
Cite this article
Brian H. Bowditch, Makoto Sakuma, The action of the mapping class group on the space of geodesic rays of a punctured hyperbolic surface. Groups Geom. Dyn. 12 (2018), no. 2, pp. 703–719
DOI 10.4171/GGD/453