Cannon--Thurston maps for Anosov foliations

Fuente: arXiv
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Main Author: Buckminster, Ellis
Format: Preprint
Published: 2026
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author Buckminster, Ellis
author_facet Buckminster, Ellis
contents Universal circles, introduced by Thurston and Calegari--Dunfield, are not well understood in general. Recently, the author together with Taylor showed that Anosov foliations with branching admit nonconjugate universal circles. We continue the study of these universal circles and show that for an Anosov foliation with branching on a hyperbolic manifold, the leftmost universal circle admits a Cannon--Thurston-type map to the ideal 2-sphere. This is a new type of construction of a Cannon--Thurston map. As a corollary, we show the fundamental group of the manifold acts on the leftmost universal circle with pseudo-Anosov dynamics.
format Preprint
id arxiv_https___arxiv_org_abs_2604_21201
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Cannon--Thurston maps for Anosov foliations
Buckminster, Ellis
Geometric Topology
Dynamical Systems
Universal circles, introduced by Thurston and Calegari--Dunfield, are not well understood in general. Recently, the author together with Taylor showed that Anosov foliations with branching admit nonconjugate universal circles. We continue the study of these universal circles and show that for an Anosov foliation with branching on a hyperbolic manifold, the leftmost universal circle admits a Cannon--Thurston-type map to the ideal 2-sphere. This is a new type of construction of a Cannon--Thurston map. As a corollary, we show the fundamental group of the manifold acts on the leftmost universal circle with pseudo-Anosov dynamics.
title Cannon--Thurston maps for Anosov foliations
topic Geometric Topology
Dynamical Systems
url https://arxiv.org/abs/2604.21201