Geometric structures in Topology, Geometry, Global Analysis and Dynamics

2022/11/13 by Christoforos Neofytidis, Neofytidis, Christoforos · 1 citation
Mathematics · #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2211.06803

openalex publication_date 2022/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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