# Rational models for automorphisms of fiber bundles

## TL;DR

This paper develops a differential graded Lie algebra model to understand the classifying space of automorphisms of fiber bundles, linking algebraic structures with topological automorphism groups.

## Contribution

It introduces a novel algebraic model for the classifying space of fiber bundle automorphisms, bridging differential graded Lie algebras with topological automorphism spaces.

## Key findings

- Constructed a dg Lie algebra model for the classifying space
- Established a correspondence between algebraic and topological automorphisms
- Provides tools for studying automorphisms via algebraic models

## Abstract

Given a fiber bundle, we construct a differential graded Lie algebra model for the classifying space of the monoid of homotopy equivalences of the base covered by a fiberwise isomorphism of the total space.