Anosov diffeomorphisms on Thurston geometric 4-manifolds

Abstract

A long-standing conjecture asserts that any Anosov diffeomorphism of a closed manifold is finitely covered by a diffeomorphism which is topologically conjugate to a hyperbolic automorphism of a nilpotent manifold. In this paper, we show that any closed 4-manifold that carries a Thurston geometry and is not finitely covered by a product of two aspherical surfaces does not support (transitive) Anosov diffeomorphisms.

13 pages; v2: final version, to appear in Geometriae Dedicata

References in corpus (4)

• Fundamental groups of aspherical manifolds and maps of non-zero degree
• Aspherical products which do not support Anosov diffeomorphisms
• Anosov diffeomorphisms of products II. Aspherical manifolds
• Anosov diffeomorphisms of products I. Negative curvature and rational homology spheres

Cited by in corpus (1)

• Geometric structures in Topology, Geometry, Global Analysis and Dynamics