Jump to content

Thin group (algebraic group theory)

Edit links
From Wikipedia, the free encyclopedia

This is an old revision of this page, as edited by K9re11 (talk | contribs) at 20:22, 10 February 2015. The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

In algebraic group theory, a thin group is a discrete Zariski-dense subgroup of G(R) that has infinite covolume, where G is a semisimple algebraic group over the reals. This is in contrast to a lattice, which is a discrete subgroup of finite covolume.

The theory of "group expansion" (expander graph properties of related Cayley graphs) for particular thin groups has been applied to arithmetic properties of Apollonian circles and in Zaremba's conjecture.[1]

References

  1. ^ http://gauss.math.yale.edu/~ho2/MSRI_Bourgain.pdf
  • Breuillard, Emmanuel; Oh, Hee, eds. (2014), Thin Groups and Superstrong Approximation, Cambridge University Press, ISBN 978-1-107-03685-7
Stub icon

This geometry-related article is a stub. You can help Wikipedia by expanding it.

Retrieved from "https://en.wikipedia.org/w/index.php?title=Thin_group_(algebraic_group_theory)&oldid=646545642"