Model geometry

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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)