Acute Geodesic Triangulations of Manifolds

Sang-hyun Kim ()
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Sang-hyun Kim: Korea Institute for Advanced Study (KIAS), School of Mathematics

Chapter Chapter 7 in In the Tradition of Thurston II, 2022, pp 261-291 from Springer

Abstract: Abstract We give a brief survey on acute geodesic triangulations of certain manifolds such as higher dimensional manifolds, Riemannian surfaces and flat cone surfaces. In the special case of a round two-sphere we review the result of the author with Walsh that gives a complete combinatorial characterization of acute geodesic triangulations. We particularly focus on results that are related with hyperbolic geometry, including Thurston’s geometric description for the Deligne–Mostow lattices and the Koebe–Andreev–Thurston theorem on circle packings. We will briefly sketch the proofs of the key results, and list relevant outstanding open problems.

Keywords: Acute geodesic triangulation; Koebe–Andreev–Thurston theorem; Polytope; Hyperbolic space; Complex hyperbolic lattice; Primary: 57M60; Secondary: 20F36, 30F45, 52B05, 65M50 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-97560-9_7

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DOI: 10.1007/978-3-030-97560-9_7

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