Volume 21, issue 6 (2017)

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

Volume 22, 1 issue

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Maximal representations, non-Archimedean Siegel spaces, and buildings

Marc Burger and Maria Beatrice Pozzetti

Geometry & Topology 21 (2017) 3539–3599
Abstract

Let F be a real closed field. We define the notion of a maximal framing for a representation of the fundamental group of a surface with values in Sp(2n, F). We show that ultralimits of maximal representations in Sp(2n, ) admit such a framing, and that all maximal framed representations satisfy a suitable generalization of the classical collar lemma. In particular, this establishes a collar lemma for all maximal representations into Sp(2n, ). We then describe a procedure to get from representations in Sp(2n, F) interesting actions on affine buildings, and in the case of representations admitting a maximal framing, we describe the structure of the elements of the group acting with zero translation length.

Keywords
maximal representation, affine building, collar lemma, real closed field, non-Archimedean symmetric spaces
Mathematical Subject Classification 2010
Primary: 20-XX, 22E40
References
Publication
Received: 4 November 2015
Revised: 15 October 2016
Accepted: 19 January 2017
Published: 31 August 2017
Proposed: Ian Agol
Seconded: Leonid Polterovich, Yasha Eliashberg
Authors
Marc Burger
Department of Mathematics
ETH Zentrum
Zürich
Switzerland
Maria Beatrice Pozzetti
Mathematics Institute
University of Warwick
Coventry
United Kingdom