Volume 21, issue 3 (2021)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21
Issue 4, 1595–2140
Issue 3, 1075–1593
Issue 2, 543–1074
Issue 1, 1–541

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Limits of sequences of pseudo-Anosov maps and of hyperbolic $3$–manifolds

Sylvain Bonnot, André de Carvalho, Juan González-Meneses and Toby Hall

Algebraic & Geometric Topology 21 (2021) 1351–1370
Abstract

There are two objects naturally associated with a braid β Bn of pseudo-Anosov type: a (relative) pseudo-Anosov homeomorphism φβ: S2 S2; and the finite-volume complete hyperbolic structure on the 3–manifold Mβ obtained by excising the braid closure of β, together with its braid axis, from S3. We show the disconnect between these objects, by exhibiting a family of braids {βq : q (0, 1 3]} with the properties that, on the one hand, there is a fixed homeomorphism φ0: S2 S2 to which the (suitably normalized) homeomorphisms φβq converge as q 0, while, on the other hand, there are infinitely many distinct hyperbolic 3–manifolds which arise as geometric limits of the form limkMβq k, for sequences qk 0.

Keywords
hyperbolic $3$–manifolds, pseudo-Anosov homeomorphisms, geometric limits
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 20F36, 37E30, 57M25
References
Publication
Received: 15 February 2019
Revised: 5 December 2019
Accepted: 8 March 2020
Published: 11 August 2021
Authors
Sylvain Bonnot
Instituto de Matemática e Estatística
Universidade de São Paulo
São Paulo
Brazil
André de Carvalho
Instituto de Matemática e Estatística
Universidade de São Paulo
São Paulo
Brazil
Juan González-Meneses
Departamento de Álgebra
Instituto de Matemáticas
Universidad de Sevilla
Sevilla
Spain
Toby Hall
Department of Mathematical Sciences
University of Liverpool
Liverpool
United Kingdom