English

Compactly presented groups

Group Theory 2010-03-23 v1

Abstract

This survey purports to be an elementary introduction to compactly presented groups, which are the analogue of finitely presented groups in the broader realm of locally compact groups. In particular, compact presentation is interpreted as a coarse simple connectedness condition on the Cayley graph, and in particular is a quasi-isometry invariant. In the appendix, an example of a Lie group, not quasi-isometric to any homogeneous graph, is given; the short argument relies on results of Trofimov and Pansu, anterior to~1990.

Keywords

Cite

@article{arxiv.1003.3959,
  title  = {Compactly presented groups},
  author = {Yves Cornulier},
  journal= {arXiv preprint arXiv:1003.3959},
  year   = {2010}
}

Comments

Preliminary version (13 pages). Comments welcome!

R2 v1 2026-06-21T15:00:18.122Z