A new boundary of the mapping class group
Lixin Liu, Yaozhong Shi
TL;DR
This paper introduces a novel boundary for the mapping class group derived from its action on measured foliations, and explores the implications for Teichmüller space compactifications and orbit closures.
Contribution
It constructs a new boundary of the mapping class group and analyzes the structure of orbit closures in various Teichmüller space compactifications.
Findings
Describes the closure of mapping class group orbits in Thurston and Gardiner-Masur compactifications.
Constructs new points in the Gardiner-Masur boundary.
Provides insights into the structure of the mapping class group's boundary.
Abstract
Based on the action of the mapping class group on the space of measured foliations, we construct a new boundary of the mapping class group and study the structure of this boundary. As an application, for any point in Teichmuller space, we consider the orbit of this point under the action of the mapping class group and describe the closure of this orbit in the Thurston compactification and the Gardiner-Masur compactification of Teichmuller space. We also construct some new points in the Gardiner-Masur boundary of Teichmuller space.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory