Geometric structures in Topology, Geometry, Global Analysis and Dynamics
Geometric Topology
2025-08-15 v2 Algebraic Topology
Differential Geometry
Dynamical Systems
Group Theory
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).
Cite
@article{arxiv.2211.06803,
title = {Geometric structures in Topology, Geometry, Global Analysis and Dynamics},
author = {Christoforos Neofytidis},
journal= {arXiv preprint arXiv:2211.06803},
year = {2025}
}
Comments
36 pages, survey chapter; v2: final version, to appear in the book "In the tradition of Thurston III", edited by K. Ohshika and A. Papadopoulos