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On homogeneous compacta in Euclidean space and the classical Hilbert-Smith conjecture. (English) Zbl 0949.57022

Tangmanee, E. (ed.) et al., Proceedings of the second Asian mathematical conference 1995, Nakhon Ratchasima, Thailand, October 17-20, 1995. Singapore: World Scientific. 222-226 (1998).
Summary: We outline the geometric approach to the Hilbert-Smith conjecture which asserts that among locally compact groups only Lie groups can act effectively on manifolds. In particular, we discuss recent results of J. Malešič, E. V. Shchepin and the authors.
For the entire collection see [Zbl 0937.00509].

MSC:

57S10 Compact groups of homeomorphisms
54F15 Continua and generalizations
54H15 Transformation groups and semigroups (topological aspects)
22E99 Lie groups
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