Compactly presented groups

Details Compactly presented groups Compactly presented groups

2010-03-21

arxiv.org/abs/1003.3959v1

Mathematics

Group Theory

Preliminary version (13 pages). Comments welcome!

Scientific paper

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.

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