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West's problem on equivariant hyperspaces and the Banach-Mazur compacta
by
Sergey Antonyan
National University of Mexico
In 1976 J. E. West asked the following question: Let G be a compact connected Lie group. Whether the orbit space (exp G)/G is an absolute retract, and if so, whether it is always homeomorphic to the Hilbert cube? Here, as usual, for a a metrizable G-space X, exp X denotes the hyperspace of all nonempty compact subsets of X endowed with the Hausdorff metric topology and with the induced action of G.
In this talk we shall present new results about equivariant hyperspaces that imply a positive solution to the first part of West's problem. Further, the relationship between West's problem above and Pelczy\'nski's problem about the Banach-Mazur compacta BM(n), n ³ 2, will be discussed. On this way we discover new properties of the Banach-Mazur compacta, for instance, we prove that the complement BM0(n) of the unique singular point in BM(n) is a Hilbert cube manifold for every n ³ 2. This is applied to obtain new topological models for BM(n). Other related results will also be discussed.
Date received: August 30, 2002
Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caje-70.