On exponential groups and Maurer–Cartan spaces

Berglund, Alexander

doi:10.1090/bproc/210

On exponential groups and Maurer–Cartan spaces
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by Alexander Berglund;

Proc. Amer. Math. Soc. Ser. B 11 (2024), 358-370

DOI: https://doi.org/10.1090/bproc/210

Published electronically: July 11, 2024

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Abstract:

The purpose of this note is to give a concise account of some fundamental properties of the exponential group and the Maurer–Cartan space associated to a complete dg Lie algebra. In particular, we give a direct elementary proof that the Maurer–Cartan space is a delooping of the exponential group. This leads to a short proof that the Maurer–Cartan space functor is homotopy inverse to Quillen’s functor from simply connected pointed spaces to positively graded dg Lie algebras.

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