Volume 20, issue 3 (2016)

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

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

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
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Higher laminations and affine buildings

Ian Le

Geometry & Topology 20 (2016) 1673–1735
Abstract

We give a Thurston-like definition for laminations on higher Teichmüller spaces associated to a surface S and a semi-simple group G for G = SLm or PGLm. The case G = SL2 or PGL2 corresponds to the classical theory of laminations on a hyperbolic surface. Our construction involves positive configurations of points in the affine building. We show that these laminations are parametrized by the tropical points of the spaces XG,S and AG,S of Fock and Goncharov. Finally, we explain how the space of projective laminations gives a compactification of higher Teichmüller space.

Keywords
higher Teichmüller theory, compactifications, tropical points, laminations, buildings, flag variety, affine Grassmannian
Mathematical Subject Classification 2010
Primary: 22E40
References
Publication
Received: 16 December 2014
Revised: 1 June 2015
Accepted: 8 July 2015
Published: 4 July 2016
Proposed: Benson Farb
Seconded: Danny Calegari, Walter Neumann
Authors
Ian Le
Department of Mathematics
University of Chicago
5734 S. University Avenue, Room 208C
Chicago, IL 60637
USA