Geometric Structures in Topology, Geometry, Global Analysis and Dynamics

Christoforos Neofytidis ()
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Christoforos Neofytidis: Ohio State University, Department of Mathematics

Chapter Chapter 9 in In the Tradition of Thurston III, 2024, pp 299-338 from Springer

Abstract: Abstract Following Thurston’s geometrisation picture in dimension three, we study geometric manifolds in a more general setting in arbitrary dimensions, with respect to the following problems: (1) The existence of maps of non-zero degree (domination relation or Gromov’s order); (2) The Gromov-Thurston monotonicity problem for numerical homotopy invariants with respect to the domination relation; (3) The existence of Anosov diffeomorphisms (Anosov-Smale conjecture).

Keywords: Thurston geometry; Aspherical manifold; Domination; Gromov order; Monotone invariant; Simplicial volume; Kodaira dimension; Anosov diffeomorphism; 57M05; 57M10; 57M50; 55M25; 22E25; 20F34; 37D20; 55R10; 57R19 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-43502-7_9

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DOI: 10.1007/978-3-031-43502-7_9

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