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

Volume 24, 1 issue

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

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
The deformation space of nonorientable hyperbolic $3$–manifolds

Juan Luis Durán Batalla and Joan Porti

Algebraic & Geometric Topology 24 (2024) 109–140
Abstract

We consider nonorientable hyperbolic 3–manifolds of finite volume M3. When M3 has an ideal triangulation Δ, we compute the deformation space of the pair (M3,Δ) (its Neumann–Zagier parameter space). We also determine the variety of representations of π1(M3) in Isom(3) in a neighborhood of the holonomy. As a consequence, when some ends are nonorientable, there are deformations from the variety of representations that cannot be realized as deformations of the pair (M3,Δ). We also discuss the metric completion of these structures and we illustrate the results on the Gieseking manifold.

Keywords
three-manifold, hyperbolic Dehn filling, nonorientable
Mathematical Subject Classification
Primary: 57K32
Secondary: 57K35, 57Q99
References
Publication
Received: 22 February 2021
Revised: 4 April 2022
Accepted: 9 August 2022
Published: 18 March 2024
Authors
Juan Luis Durán Batalla
Departament de Matemàtiques
Universitat Autònoma de Barcelona
Barcelona
Spain
Joan Porti
Departament de Matemàtiques
Universitat Autònoma de Barcelona, and Centre de Recerca Matemàtica
Barcelona
Spain
https://mat.uab.cat/~porti/

Open Access made possible by participating institutions via Subscribe to Open.