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On exponential groups and Maurer-Cartan spaces (2305.06904v1)
Published 11 May 2023 in math.AT
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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