1,619 research outputs found
Equivariant extension properties of coset spaces of locally compact groups and approximate slices
We prove that for a compact subgroup of a locally compact Hausdorff group
, the following properties are mutually equivalent: (1) is a manifold,
(2) is finite-dimensional and locally connected, (3) is locally
contractible, (4) is an ANE for paracompact spaces, (5) is a
metrizable -ANE for paracompact proper -spaces having a paracompact orbit
space. A new version of the Approximate slice theorem is also proven in the
light of these results
Homotopy characterization of G-ANR\u27s
Let G be a compact Lie group. We prove that if each point x X of a G-space X admits a Gx-invariant neighborhood U which is a Gx-ANE then X is a G-ANE, where Gx stands for the stabilizer of x. This result is further applied to give two equivariant homotopy characterizations of G-ANR\u27s. One of them sounds as follows: a metrizable G-space Y is a G-ANR iff Y is locally G-contractible and every metrizable closed G-pair (X, A) has the G-equivariant homotopy extension property with respect to Y. In the same terms we also characterize G-ANR subsets of a given G-ANR space
Park--Tarter Matrix for a Dyon--Dyon System
The problem of separation of variables in a dyon--dyon system is discussed. A
linear transformation is obtained between fundamental bases of this system.
Comparison of the dyon--dyon system with a 4D isotropic oscillator is carried
out.Comment: 9 pages, LaTeX fil
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