Model geometry

From Diffgeom
Revision as of 19:49, 18 May 2008 by Vipul (talk | contribs) (1 revision)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Definition

A model geometry (G,X) is a manifold X together with a Lie group G of diffeomorphisms of X such that:

  1. X is connected and simply connected
  2. G acts transitively on X, with compact point stabilizers
  3. G is not contained in any larger group of diffeomorphisms of X with compact point-stabilizers
  4. There exists at least one compact manifold modeled on (G,X)