Discontinuous Groups for Non-Riemannian Homogeneous Spaces

Toshiyuki Kobayashi

A chapter in Mathematics Unlimited — 2001 and Beyond, 2001, pp 723-747 from Springer

Abstract: Abstract A Lie group is a group G equipped with the structure of a C∞-manifold such that the multiplication $$ G \times G \to G,\quad (x,y) \mapsto x{{y}^{{ - 1}}} $$ is a C∞ map. In the definition, C∞ can be replaced by any of C0, C1, …, Cw (real analytic), by an affirmative answer of Hilbert’s fifth problem in 1900 (and von Neumann’s formulation in 1933 [48]) due to Gleason, Montgomery and Zippin in 1952.

Date: 2001
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DOI: 10.1007/978-3-642-56478-9_37

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