English

Maximal representations in lattices of the symplectic group

Geometric Topology 2025-02-18 v2 Group Theory Number Theory

Abstract

We prove that all lattices of Sp(2n,R), except those commensurable with Sp(4k+2,Z) when n=2k+1, contain the image of infinitely many mapping class group orbits of Zariski-dense maximal representation that are continuous deformations of maximal diagonal representations. In particular, we show that Sp(4k,Z) contain Zariski-dense surface subgroups for all k.

Keywords

Cite

@article{arxiv.2307.06791,
  title  = {Maximal representations in lattices of the symplectic group},
  author = {Jacques Audibert},
  journal= {arXiv preprint arXiv:2307.06791},
  year   = {2025}
}

Comments

17 pages, comments are welcome