On exponential groups and Maurer-Cartan spaces
Algebraic Topology
2023-05-12 v1
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.
Keywords
Cite
@article{arxiv.2305.06904,
title = {On exponential groups and Maurer-Cartan spaces},
author = {Alexander Berglund},
journal= {arXiv preprint arXiv:2305.06904},
year = {2023}
}
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12 pages