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2016 Higher laminations and affine buildings
Ian Le
Geom. Topol. 20(3): 1673-1735 (2016). DOI: 10.2140/gt.2016.20.1673

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.

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Ian Le. "Higher laminations and affine buildings." Geom. Topol. 20 (3) 1673 - 1735, 2016. https://doi.org/10.2140/gt.2016.20.1673

Information

Received: 16 December 2014; Revised: 1 June 2015; Accepted: 8 July 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1348.30023
MathSciNet: MR3523066
Digital Object Identifier: 10.2140/gt.2016.20.1673

Subjects:
Primary: 22E40

Rights: Copyright © 2016 Mathematical Sciences Publishers

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Vol.20 • No. 3 • 2016
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