Surface groups in uniform lattices of some semi-simple groups

Jeremy Kahn, François Labourie, Shahar Mozes

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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.

Original languageAmerican English
Pages (from-to)79-220
Number of pages142
JournalActa Mathematica
Issue number1
StatePublished - 2024

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© 2024, Rev. Bras. Eng. Agric. Ambient. All rights reserved.

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