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Mathematics Colloquium


Date:  Tuesday, October 13, 2009

Title:  Complete affine 3-manifolds and hyperbolic structures on surfaces

Abstract:  Flat Riemannian manifolds arse quotients of Euclidean space by discrete groups of isometries, and correspond to classical crystallographic groups. Such structures can equivalently be defined as systems of local coordinates into affine space where the coordinate changes are locally isometries. The theorems of Bieberbach provide an effective classification of such structures. Analogous questions for manifolds with flat connections, or equivalently, quotients by groups of affine transformations are considerably more difficult, and presently unsolved. In this talk I will describe how the classification in dimension three, reduces to a question on hyperbolic geometry on open 2-manifolds.

Speaker:  William Goldman
Institution:  Univ of Maryland


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