(Non-)existence of Cannon-Thurston maps for Morse boundaries
Ruth Charney, Matthew Cordes, Antoine Goldsborough, Alessandro Sisto,, Stefanie Zbinden
TL;DR
This paper investigates the existence of Cannon-Thurston maps for Morse boundaries, revealing cases where such maps exist and do not, contrasting with the hyperbolic setting.
Contribution
It demonstrates the nuanced behavior of Cannon-Thurston maps in Morse boundaries, highlighting both existence and non-existence scenarios.
Findings
Morse boundary can have both existence and non-existence of Cannon-Thurston maps.
Contrasts with the hyperbolic case where such maps are more uniformly understood.
Provides new examples and insights into the structure of Morse boundaries.
Abstract
We show that the Morse boundary exhibits interesting examples of both the existence and non-existence of Cannon-Thurston maps for normal subgroups, in contrast with the hyperbolic case.
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
TopicsMathematical Dynamics and Fractals · Geometric Analysis and Curvature Flows · Geometric and Algebraic Topology