An EZ-structure for the mapping class group
Ursula Hamenst\"adt
TL;DR
This paper constructs a boundary for the mapping class group of a surface, demonstrating its minimal and strongly proximal action, and establishing an EZ-structure for the group.
Contribution
It introduces a new boundary construction for the mapping class group, providing an EZ-structure that enhances understanding of its geometric and dynamical properties.
Findings
The boundary of Mod(S) is minimal and strongly proximal.
The action of Mod(S) on this boundary is topologically free.
The boundary forms an EZ-structure for Mod(S).
Abstract
We construct a boundary for the mapping class group Mod(S) of a surface S of finite type. The action of Mod(S) on this boundary is minimal, strongly proximal and topologically free. The boundary is the boundary of an EZ-structure for Mod(S).
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Taxonomy
TopicsGeometric and Algebraic Topology · Rings, Modules, and Algebras · Homotopy and Cohomology in Algebraic Topology