A dg Lie model for relative homotopy automorphisms

TL;DR

This paper develops a differential graded Lie algebra model to understand the homotopy automorphisms of a space relative to a subspace, providing a new algebraic framework for these topological transformations.

Contribution

It introduces a dg Lie model for the universal cover of the classifying space of relative homotopy automorphisms, advancing algebraic tools in homotopy theory.

Findings

Constructed a dg Lie model for the classifying space of relative homotopy automorphisms.

Provides algebraic descriptions of automorphism groups fixing a subspace.

Enhances understanding of the algebraic structure underlying relative homotopy automorphisms.

Abstract

We construct a dg Lie model for the universal cover of the classifying space of the grouplike monoid of homotopy automorphisms of a space that fix a given subspace.