Kleinian groups with ubiquitous surface subgroups
Joseph D. Masters
TL;DR
This paper proves that all finitely-generated free subgroups within certain Kleinian reflection groups are contained in surface subgroups, revealing a widespread presence of surface subgroups in these groups.
Contribution
It establishes that every finitely-generated free subgroup of a specific class of Kleinian reflection groups is contained in a surface subgroup, a novel structural insight.
Findings
Finitely-generated free subgroups are contained in surface subgroups
Surface subgroups are ubiquitous in these Kleinian groups
The result applies to right-angled, co-compact Kleinian reflection groups
Abstract
We show that every finitely-generated free subgroup of a right-angled, co-compact Kleinian reflection group is contained in a surface subgroup.
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Taxonomy
TopicsGeometric and Algebraic Topology · Finite Group Theory Research · Geometric Analysis and Curvature Flows