On the exponent of $G$-spaces and isovariant extensors

S. M. Ageev

Sbornik. Mathematics, Tome 207 (2016) no. 2, pp. 155-190

Résumé

The equivariant version of the Curtis-Schori-West theorem is investigated. It is proved that for a nondegenerate Peano $G$-continuum $\mathbb X$ with an action of the compact abelian Lie group $G$, the exponent $\exp\mathbb X$ is equimorphic to the maximal equivariant Hilbert cube if and only if the free part $\mathbb X_{\mathrm{free}}$ is dense in $\mathbb X$. We also show that the latter is sufficient for the equimorphy of $\exp\mathbb X$ and $\mathbb Q$ in the case of an action of an arbitrary compact Lie group $G$. The key to the proof of these results lies in the theory of the universal $G$-space (in the sense of Palais). Bibliography: 28 titles.

Détail

Keywords: isovariant absolute extensor, classifying $G$-space, exponent of $G$-space
Mots-clés : Palais universal $G$-space, equivariant Hilbert cube.