Klein-Maskit combination theorem for Anosov subgroups: Amalgams
Subhadip Dey, Michael Kapovich
TL;DR
This paper extends classical Klein-Maskit combination theorems to the setting of Anosov subgroups, providing new methods to construct complex groups from simpler ones using amalgams and HNN extensions.
Contribution
It introduces analogs of the Klein-Maskit combination theorems for Anosov subgroups, expanding the toolkit for constructing and analyzing these groups.
Findings
Established conditions for amalgamated free products of Anosov subgroups.
Developed analogs of HNN extension theorems for Anosov subgroups.
Provided new examples of complex Anosov groups through combination techniques.
Abstract
The classical Klein-Maskit combination theorems provide sufficient conditions to construct new Kleinian groups using old ones. There are two distinct but closely related combination theorems: The first deals with amalgamated free products, whereas the second deals with HNN extensions. This article gives analogs of both combination theorems for Anosov subgroups.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Mathematical Dynamics and Fractals · Geometric and Algebraic Topology