Higher laminations and affine buildings

Ian Tuan-Yen Le*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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 D SLm or PGLm. The case G D 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.

Original languageEnglish (US)
Pages (from-to)1673-1735
Number of pages63
JournalGeometry and Topology
Volume20
Issue number3
DOIs
StatePublished - Jul 4 2016

ASJC Scopus subject areas

  • Geometry and Topology

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