Original scientific paper

https://doi.org/10.3336/gm.42.1.05

Homotopy characterization of G-ANR's

Natella Antonyan ; Departamento de Matemáticas, Division de Ingenieria y Arquitectura, Instituto Tecnológico y de Estudios Superiores de Monterrey, Campus Ciudad de México, 14380 México Distrito Federal, México
Sergey A. Antonyan ; Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510 México Distrito Federal, México
Alejandra Soria-Pérez ; Escuela de Matemáticas, Universidad Juárez del Estado de Durango, 34120 Durango, Dgo., México

Abstract

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's. 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.

Keywords

G-ANR; G-homotopy; G-homotopy extension theorem; slice

Hrčak ID:

12882

URI

https://hrcak.srce.hr/12882

Publication date:

12.6.2007.

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