Locally Homogeneous Geometric Manifolds

By William M. Goldman. 2010

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Motivated by Felix Klein’s notion that geometry is governed by its group of symmetry transformations, Charles Ehresmann initiated the study of geometric structures on topological spaces locally modeled on a homogeneous space of a Lie group. These locally homogeneous spaces later formed the context of Thurston’s 3-dimensional geometrization program. The basic problem is for a given topology and a geometry

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c8bd5fbebcabf5a5216668e8ebe417bb4906f3e8