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Mat. Sb., 2019, Volume 210, Number 10, Pages 91–98 (Mi msb9133)  

On equivariant fibrations of $G$-CW-complexes

P. S. Gevorgyana, R. Jimenezb

a Moscow Pedagogical State University, Moscow, Russia
b Institute of Mathematics, National Autonomous University of Mexico, Oaxaca, Mexico

Abstract: It is proved that if $G$ is a compact Lie group, then an equivariant Serre fibration of $G$-CW-complexes is an equivariant Hurewicz fibration in the class of compactly generated $G$-spaces. In the nonequivariant setting, this result is due to Steinberger, West and Cauty. The main theorem is proved using the following key result: a $G$-CW-complex can be embedded as an equivariant retract in a simplicial $G$-complex. It is also proved that an equivariant map $p\colon E\to B$ of $G$-CW-complexes is a Hurewicz $G$-fibration if and only if the $H$-fixed point map $p^H\colon E^H \to B^H$ is a Hurewicz fibration for any closed subgroup $H$ of $G$. This gives a solution to the problem of James and Segal in the case of $G$-CW-complexes.
Bibliography: 9 titles.

Keywords: $G$-CW-complex, simplicial $G$-complex, equivariant fibration, $H$-fixed points.

Funding Agency Grant Number
PASPA-DGAPA, UNAM y SEP-CONACyT 284621
The research of R. Jimenez was partially supported by the Programa de Apoyos para la Superación del Personal Académico de la Dirección General de Asuntos del Personal Académico de la Universidad Nacional Autónoma de México, the Secretaría de Educación Pública and the Consejo Nacional de Ciencia y Tecnología (grant no. 284621).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm9133

Full text: PDF file (508 kB)
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English version:
Sbornik: Mathematics, 2019, 210:10, 1428–1433

Bibliographic databases:

UDC: 515.122.4
MSC: 55R91, 57S05
Received: 14.05.2018 and 20.12.2018

Citation: P. S. Gevorgyan, R. Jimenez, “On equivariant fibrations of $G$-CW-complexes”, Mat. Sb., 210:10 (2019), 91–98; Sb. Math., 210:10 (2019), 1428–1433

Citation in format AMSBIB
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