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Geometry and Model Theory

Time: Friday, May 06, 2011, 11h - 12h30

Location: ENS, salle W

Hilbert's fifth problem and applications

Isaac Goldbring (UCLA)

Hilbert's fifth problem asks whether every locally euclidean group G can be equipped with a real analytic structure (compatible with the topology) so that the group operations become real analytic; in short, is every locally euclidean group a Lie group? An affirmative answer to this question was given by Gleason, Montgomery, and Zippin in 1952. In 1990, Hirschfeld simplified the GMZ proof by using the methods of nonstandard analysis. There is also a local version of Hilbert's fifth problem (local H5), namely whether every locally euclidean local group is locally isomorphic to a Lie group. The local H5 has an interesting history and was settled in my Ph.D. thesis by adapting Hirschfeld's nonstandard techniques. In this talk, I will discuss both the global and local versions of the H5 and discuss a few of their applications.


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