Classification of fiber sequences with a prescribed holonomy action

TL;DR

This paper introduces a classification framework for fiber sequences with a specific holonomy action constrained within a subgroup of the homotopy automorphism group, expanding understanding of fiber bundle structures.

Contribution

It defines $ ext{H}$-fibration sequences with prescribed holonomy actions and provides a universal classification for these sequences.

Findings

Defined $ ext{H}$-fibration sequences with specific holonomy constraints

Developed a universal $ ext{H}$-fibration sequence for classification

Extended the theory of fiber sequences with controlled automorphism actions

Abstract

We define $\mathcal{H}$-fibration sequences as fibrations where the holonomy action of the fundamental group of the base on the fiber lies in a given subgroup $\mathcal{H}$ of $\mathcal{E}(F)$, where $\mathcal{E}(F)$ is the homotopy automorphism group of the fiber. Furthermore, we classify these $\mathcal{H}$-fibration sequences via a universal $\mathcal{H}$-fibration sequence.