Volume 22, issue 7 (2018)

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

Volume 27
Issue 8, 2937–3385
Issue 7, 2497–2936
Issue 6, 2049–2496
Issue 5, 1657–2048
Issue 4, 1273–1655
Issue 3, 823–1272
Issue 2, 417–821
Issue 1, 1–415

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Volumes of $\mathrm{SL}_n(\mathbb{C})$–representations of hyperbolic $3$–manifolds

Wolfgang Pitsch and Joan Porti

Geometry & Topology 22 (2018) 4067–4112

Let M be a compact oriented three-manifold whose interior is hyperbolic of finite volume. We prove a variation formula for the volume on the variety of representations of π1(M) in SLn(). Our proof follows the strategy of Reznikov’s rigidity when M is closed; in particular, we use Fuks’s approach to variations by means of Lie algebra cohomology. When n = 2, we get Hodgson’s formula for variation of volume on the space of hyperbolic Dehn fillings. Our formula also recovers the variation of volume on the space of decorated triangulations obtained by Bergeron, Falbel and Guilloux and Dimofte, Gabella and Goncharov.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

volume, hyperbolic manifold, characteristic class, representation variety, Schäfli formula, flat bundle
Mathematical Subject Classification 2010
Primary: 14D20, 57M50
Secondary: 57R20, 57T10
Received: 19 April 2017
Revised: 21 March 2018
Accepted: 20 May 2018
Published: 6 December 2018
Proposed: Walter Neumann
Seconded: Ian Agol, Bruce Kleiner
Wolfgang Pitsch
BGSMath and Departament de Matemàtiques
Universitat Autònoma de Barcelona
Joan Porti
BGSMath and Departament de Matemàtiques
Universitat Autònoma de Barcelona