Original scientific paper

Fiberwise retraction and shape properties of the orbit space

Sergey A. Antonyan
Rolando Jimenez
Sylvia de Neymet

Abstract

From the point of view of retracts and shape theory, the category G-TOPB of G-spaces over a G-space B, where G is a compact group, is investigated. In particular, we prove that if B has only one orbit type and E is a metric G-ANR over B, then the orbit space E/G is an ANR over B/G. As an application we construct a fiberwise G-orbit functor μ : G-SHB → SHB/G on shape level.

Keywords

Equivariant rectract; equivariant fiberwise shape; orbit space; G-ANR; G-shape; G-resolution

Hrčak ID:

4870

URI

https://hrcak.srce.hr/4870

Publication date:

1.12.2000.

Visits: 1.052 *