2018/05/25 by Jeremy Kahn, Kahn, Jeremy, François Labourie +3 · 3 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry #Group (periodic table) #Mathematics #Physics #Pure mathematics #Quantum mechanics #Simple (philosophy) #Simple group #Surface (topology) #math.DG
paper · pdf · doi:10.48550/arxiv.1805.10189
published in arXiv (Cornell University) (Cornell University) · 91 pages, 21 figures, v5: many typos, inaccuracies have been corrected. Section 9 and 11 underwent major changes. Th. 9.2.4 (in v4) was wrong. This theorem was used in Th. 11.4.1.itself used in Th. 16.3.1, In v5, Th.11.4.1. (and 11.4.4) is now weaker. Using a new argument section 16.2 we get Th. 16.3.1 with the same generality
openalex publication_date 2018/05/25 · arxiv created 2020/11/17 · arxiv updated 2020/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.