Geometrization of Piecewise homeomorphisms of the circle
J\'er\^ome Los, Natalia A. Viana Bedoya

TL;DR
This paper investigates the conditions under which certain piecewise circle homeomorphisms can be realized as Bowen-Series maps linked to surface groups, connecting geometric and dynamical properties.
Contribution
It characterizes the geometric and dynamical criteria needed for realizing piecewise homeomorphisms as Bowen-Series-like maps for surface groups.
Findings
Identifies sufficient conditions for realization as Bowen-Series maps
Links geometric properties to dynamical realizability
Provides a framework for understanding circle homeomorphisms in geometric group theory
Abstract
In this work we study the following realization problem: given a piecewise homeomorphism , which geometrical and dynamical conditions on are sufficient to realize it as a Bowen-Series-like map associated to a surface group, seen as a discrete subgroup of ?
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Mathematics and Applications
