English

Anosov representations and dominated splittings

Group Theory 2020-05-04 v3 Dynamical Systems Metric Geometry

Abstract

We provide a link between Anosov representations introduced by Labourie and dominated splitting of linear cocycles. This allows us to obtain equivalent characterizations for Anosov representations and to recover recent results due to Gu\'eritaud-Guichard-Kassel-Wienhard and Kapovich-Leeb-Porti by different methods. We also give characterizations in terms of multicones and cone-types inspired in the work of Avila-Bochi-Yoccoz and Bochi-Gourmelon. Finally we provide a new proof of the higher rank Morse Lemma of Kapovich-Leeb-Porti.

Cite

@article{arxiv.1605.01742,
  title  = {Anosov representations and dominated splittings},
  author = {Jairo Bochi and Rafael Potrie and Andrés Sambarino},
  journal= {arXiv preprint arXiv:1605.01742},
  year   = {2020}
}

Comments

Published version. A wrong claim about cone types in Sec. 5.3 was struck out; this claim wasn't used

R2 v1 2026-06-22T13:54:16.346Z