Surface groups in uniform lattices of some semi-simple groups (François Labourie, Nice)

27.11.2018 10:30

We show that uniform lattices in some semi-simple groups (notably complex ones) admit Anosov surface subgroups. This result has a quantitative version: we introduce a notion, called K-Sullivan maps, which generalizes the notion of K-quasi-circles in hyperbolic geometry, and show in particular that Sullivan maps are Hölder. Using this notion, we show a quantitative version of our surface subgroup theorem and in particular that one can obtain K-Sullivan limit maps, as close as one wants to smooth round circles. All these results use the coarse geometry of "path of triangles" in a certain flag manifold and we prove an analogue to the Morse Lemma for quasi-geodesics in that context.

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Room 17 (Att. unusual room), Séminaire "Groupes et Géométrie"

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