Séminaire Géométrie et groupes discrets

Positivity, Cross-ratios and the Collar Lemma

by François Labourie (Université Côte d'Azur)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

I will explain why positive representations of fundamental groups of surfaces satisfy a "collar lemma" similar to the classical collar lemma for hyperbolic geometry, and have associated positive cross-ratios. As a consequence, I will deduce that positive representations form closed subsets of the representation variety. I will spend some time recalling what a positive representation is, what the associated cross-ratios are, and explain the main new object that we shall use and that we call "photons". This is joint work with Jonas Beyrer, Olivier Guichard, Beatrice Pozzetti and Anna Wienhard.

Organized by

Fanny Kassel