Geometric structures in Topology, Geometry, Global Analysis and Dynamics

Christoforos Neofytidis

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

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arXiv · 2211.06803

Geometric structures in Topology, Geometry, Global Analysis and Dynamics

Christoforos Neofytidis

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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: (i) The existence of maps of non-zero degree (domination relation or Gromov's order); (ii) The Gromov-Thurston monotonicity problem for numerical homotopy invariants with respect to the domination relation; (iii) The existence of Anosov diffeomorphisms (Anosov-Smale conjecture).

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Christoforos Neofytidis. 2022-11-13. Geometric structures in Topology, Geometry, Global Analysis and Dynamics. https://doi.org/10.1007/978-3-031-43502-7_9

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