Anosov diffeomorphisms of products II. Aspherical manifolds

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Neofytidis, Christoforos¹ 

[1] Univ Geneva, Sect Math, 2-4 Rue Lievre,Case Postale 64, CH-1211 Geneva 4, Switzerland

关键词: Anosov diffeomorphism;    Direct product;    Aspherical manifold;    Trivial center;    Finite outer automorphism group;    Hopf property;   

DOI  :  10.1016/j.jpaa.2019.07.005

来源: Elsevier

【 摘 要 】

We study aspherical manifolds that do not support Anosov diffeomorphisms. Weakening conditions of Gogolev and Lafont, we show that the product of an infranilmanifold with finitely many aspherical manifolds whose fundamental groups have trivial center and finite outer automorphism group does not support Anosov diffeomorphisms. In the course of our study, we obtain a result of independent group theoretic and topological interest on the stability of the Hopf property, namely, that the product of finitely many Hopfian groups with trivial center is Hopfian. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free