2,228 research outputs found
Regular Lie groups and a theorem of Lie-Palais
In 1984 Milnor had shown how to deduce the Lie-Palais theorem on integration
of infinitesimal actions of finite-dimensional Lie algebras on compact
manifolds from general theory of regular Lie groups modelled on locally convex
spaces. We show how, in the case of effective action, one can eliminate from
Milnor's argument the abstract Lie-Cartan theorem, making the deduction rather
elementary. A machinery employed in the proof provides a partial solution to a
problem examined in 1972 by van Est and \'Swierczkowski.Comment: 5 pages. AmS TeX 2.1 source fil
A theorem of Hrushovski-Solecki-Vershik applied to uniform and coarse embeddings of the Urysohn metric space
A theorem proved by Hrushovski for graphs and extended by Solecki and Vershik
(independently from each other) to metric spaces leads to a stronger version of
ultrahomogeneity of the infinite random graph , the universal Urysohn metric
space \Ur, and other related objects. We show how the result can be used to
average out uniform and coarse embeddings of \Ur (and its various
counterparts) into normed spaces. Sometimes this leads to new embeddings of the
same kind that are metric transforms and besides extend to affine
representations of various isometry groups. As an application of this
technique, we show that \Ur admits neither a uniform nor a coarse embedding
into a uniformly convex Banach space.Comment: 23 pages, LaTeX 2e with Elsevier macros, a significant revision
taking into account anonymous referee's comments, with the proof of the main
result simplified and another long proof moved to the appendi
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