# '22

36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

### "G-maps over the homogeneous space G/H as equivariant fibrations"

#### Kantún-Montiel, Aura Lucina

By a $G$-fibration, we mean the equivariant version of a Hurewicz fibration, that is, a $G$-map having the equivariant homotopy lifting property with respect to all $G$-spaces. $G$-fibrations arise in equivariant theory quite naturally, one of the classical results states that if $H$ is a closed subgroup of a compact Lie group $G$, then any $G$-map $q:E\rightarrow G/H$ is a $G$-fibration. A natural question is whether this result remains valid when working with a non-compact or non-Lie acting group. To answer this, we are going to give generalizations of some classical results that lead us to prove that $p$ is also a $G$-fibration whenever $G$ is a (not necessarily compact) Lie group or an almost connected metrizable group and $H$ its compact subgroup. In fact, we have a more general result: If $p:E\rightarrow B$ is an $H$-fibration, then the $G$-map induced by the twisted product functor $G\times_H E\rightarrow G\times_H B$ is a $G$-fibration.

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