On projective Anosov subgroups of symplectic groups

Author:

Pozzetti Maria Beatrice1,Tsouvalas Konstantinos2ORCID

Affiliation:

1. Mathematical Institute Heidelberg University Heidelberg Germany

2. Max Planck Institute for Mathematics in the Sciences Leipzig Germany

Abstract

AbstractWe prove that a word hyperbolic group whose Gromov boundary properly contains a 2‐sphere cannot admit a projective Anosov representation into , . We also prove that a word hyperbolic group that admits a projective Anosov representation into is virtually a free group or virtually a surface group, a result established independently by Dey–Greenberg–Riestenberg.

Funder

Deutsche Forschungsgemeinschaft

European Research Council

Publisher

Wiley

Subject

General Mathematics

Reference15 articles.

1. Anosov representations and dominated splittings

2. Quasi-hyperbolic planes in hyperbolic groups

3. R. D.Canary Informal lecture notes on Anosov representations available at:http://www.math.lsa.umich.edu/canary/ 2021.

4. Topological restrictions on Anosov representations

5. S.Dey Z.Greenberg andJ. M.Riestenberg Restrictions on Anosov subgroups ofSp(2n R)$\mathsf {Sp}(2n \mathbb {R})$ arXiv:2304.13564 2023.

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