Subgroups of the mapping class group from the geometrical viewpoint
Richard P. Kent IV, Christopher J. Leininger
TL;DR
This paper explores the analogy between Kleinian groups and subgroups of the mapping class group of a surface from a geometric perspective, providing a survey of related concepts and results.
Contribution
It offers a comprehensive survey highlighting the geometric similarities and differences between Kleinian groups and mapping class subgroups.
Findings
Identifies key geometric properties linking the two classes of groups
Summarizes recent advances in understanding subgroup structures
Highlights open problems and future research directions
Abstract
We survey the analogy between Kleinian groups and subgroups of the mapping class group of a surface.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Homotopy and Cohomology in Algebraic Topology