Structural foundations for equivariant fibration theorems

Abstract

We study several structural properties that determine when projections between homogeneous spaces give rise to equivariant fibrations. We focus on three key conditions: the projection viewed as a conjugate H-fibration, the preservation of fibrations under the twisted-product functor , and a straightening condition for G-homeomorphisms of the form . We prove that the first two conditions are equivalent, and that the third one provides a general mechanism for establishing the second one. This yields a unified framework for proving equivariant fibration theorems beyond the classical compact Lie group setting.