A fake Schottky group in Mod(S)
Richard P. Kent IV, Christopher J. Leininger
TL;DR
This paper constructs non-Schottky subgroups within the mapping class group using classical hyperbolic geometry methods, challenging the typical understanding of Schottky groups.
Contribution
It introduces a novel approach to identify non-Schottky subgroups in the mapping class group through hyperbolic geometric constructions.
Findings
Existence of non-Schottky subgroups in Mod(S) demonstrated.
Application of hyperbolic geometry to group theory.
New insights into subgroup structures of the mapping class group.
Abstract
We use the classical construction of Schottky groups in hyperbolic geometry to produce non-Schottky subgroups of the mapping class group.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Finite Group Theory Research