The number of ends of big mapping class groups
Josiah Oh, Yulan Qing, Xiaolei Wu
TL;DR
This paper investigates the number of ends of big mapping class groups, establishing conditions under which they are one-ended based on properties of the associated curve graph.
Contribution
It proves that the mapping class group is one-ended if the stable avenue surface has at least one end of discrete type, using the quasi-isometry with the curve graph.
Findings
Mapping class group is one-ended under certain conditions.
The associated curve graph is quasi-isometric to the mapping class group.
The method links the ends of the surface to the ends of the group.
Abstract
We analyze the number of ends of the mapping class group of a stable avenue surface. We prove that the mapping class group is one-ended whenever the stable avenue surface has at least one end of discrete type. Our method is to show that the associated translatable curve graph, which is quasi-isometric to the mapping class group, is one-ended.
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Taxonomy
TopicsGeometric and Algebraic Topology · Geometric Analysis and Curvature Flows · Computational Geometry and Mesh Generation