Vol. 82, No. 2, 1979

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On the topology and geometry of arcwise connected, finite-dimensional groups

Sigmund Nyrop Hudson

Vol. 82 (1979), No. 2, 429–450

If G is an arcwise connected, finite-dimensional group, then it is known that there exists a connected Lie group G and a continuous, one-one, onto homomorphism i : GG. Results are obtained for describing the topology of G in terms of the geometry of the manifold G and of i. The major result is that there is a closed subgroup S of G and arbitrarily small neighborhoods U at the identity of G such that there are real numbers r and s satisfying i1(U) is the union of mutually disjoint open balls in G of radius r scattered along the submanifold S in such a manner that the balls are separated by at least s. In the case that G is embedded in a locally compact group, more detailed information is given for the distribution of the open balls in G.

Mathematical Subject Classification 2000
Primary: 22A05
Received: 13 March 1978
Revised: 17 July 1978
Published: 1 June 1979
Sigmund Nyrop Hudson