Relations between Non-Compact Transformation Groups and Compact Transformation Groups

Introduction to Compact Transformation Groups

Disintegration of Measures on Compact Transformation Groups

To prove 1.1, one first assumes X is compact and G is a Lie group. In this case, X is "measure-theoretically" the product Y x G; this follows from the existence of local cross-sections to the projection n [6]. Let n2 : X ~ Y x G —> G, and define a map £ from L(Y, v) to the space of Radon measures on G as follows: £(ƒ) = TÏ2 [if ° n) ' M] • Apply the Dunford-Pettis Theorem [3] to ? to obtain a m...

On Locally Lipschitz Locally Compact Transformation Groups of Manifolds

In this paper we show that a “locally Lipschitz” locally compact transformation group acting continuously and effectively on a connected paracompact locally Euclidean topological manifold is a Lie group. This is a contribution to the proof of the Hilbert-Smith conjecture. It generalizes the classical Bochner-Montgomery-Kuranishi Theorem[1, 9] and also the Repovš-Ščepin Theorem [17] which holds ...

The Covering Homotopy Extension Problem for Compact Transformation Groups

It is shown that the orbit space of universal (in the sense of Palais) G-spaces classifies G-spaces. Theorems on the extension of covering homotopy for G-spaces and on a homotopy representation of the isovariant category ISOV are proved . DOI: 10.1134/S0001434612110016

On component extensions locally compact abelian groups

Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...