Higher laminations and affine buildings

Le, Ian¹

¹ Department of Mathematics, University of Chicago, 5734 S. University Avenue, Room 208C, Chicago, IL 60637, USA

Geometry & topology, Tome 20 (2016) no. 3, pp. 1673-1735.

Résumé

We give a Thurston-like definition for laminations on higher Teichmüller spaces associated to a surface $S$ and a semi-simple group $G$ for $G={SL}_m$ or ${PGL}_m$. The case $G={SL}_2$ or ${PGL}_2$ 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 ${\mathcal{X}}_{G,S}$ and ${\mathcal{A}}_{G,S}$ of Fock and Goncharov. Finally, we explain how the space of projective laminations gives a compactification of higher Teichmüller space.

Détail

DOI : 10.2140/gt.2016.20.1673

Classification : 22E40
Keywords: higher Teichmüller theory, compactifications, tropical points, laminations, buildings, flag variety, affine Grassmannian

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