Equivariant extension properties of coset spaces of locally compact groups and approximate slices

We prove that for a compact subgroup $H$ of a locally compact Hausdorff group $G$, the following properties are mutually equivalent: (1) $G/H$ is a manifold, (2) $G/H$ is finite-dimensional and locally connected, (3) $G/H$ is locally contractible, (4) $G/H$ is an ANE for paracompact spaces, (5) $G/H$ is a metrizable $G$-ANE for paracompact proper $G$-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