Homology, Homotopy and Applications

Volume 22 (2020)

Number 2

A $\operatorname{dg}$ Lie model for relative homotopy automorphisms

Pages: 105 – 121

DOI: https://dx.doi.org/10.4310/HHA.2020.v22.n2.a6


Alexander Berglund (Department of Mathematics, Stockholm University, Stockholm, Sweden)

Bashar Saleh (Department of Mathematics, Stockholm University, Stockholm, Sweden)


We construct a $\operatorname{dg}$ Lie algebra model for the universal cover of the classifying space of the grouplike monoid of homotopy automorphisms of a space that fix a given subspace. We derive the model from a known model for based homotopy automorphisms together with general result on rational models for geometric bar constructions.


homotopy automorphism, rational homotopy theory, Lie models

2010 Mathematics Subject Classification


Received 11 July 2019

Accepted 14 September 2019

Published 25 March 2020