G-compactifications of pseudocompact G-spaces

Equivariant Embeddings and Compactifications of Free G-spaces

For a compact Lie group G, we characterize free G-spaces that admit free Gcompactifications. For such G-spaces, a universal compact free G-space of given weight and given dimension is constructed. It is shown that if G is finite, the ndimensional Menger free G-compactum μn is universal for all separable, metrizable free G-spaces of dimension less than or equal to n. Some of these results are ex...

Pseudocompact Spaces

Equivariant Embedding of Metrizable G-spaces in Linear G-spaces

Given a Lie group G we study the class MG of proper metrizable G-spaces with metrizable orbit spaces, and show that any G-space X ∈ MG admits a closed G-embedding into a convex G-subset C of some locally convex linear G-space, such that X has some G-neighborhood in C which belongs to the class MG. As a corollary we see that any G-ANR for MG is a G-ANE for MG.

Calibrations on spaces with G×G–structure

In these notes we give an introduction to the concept of spaces with G×G–structure and their structured submanifolds. These objects generalise the classical notion of a calibrated submanifold. Therefore, they are interesting from a string theory viewpoint as they are relevant to describe D–branes in string compactifica-tions on backgrounds with fluxes.

The concentration function problem for $G$-spaces

‎In this note‎, ‎we consider the concentration function problem for a continuous action of a locally compact group $G$ on a locally compact Hausdorff space $X$‎. ‎We prove a necessary and sufficient condition for the concentration functions of a‎ ‎spread-out irreducible probability measure $mu$ on $G$ to converge to zero.