Algebraic models of non-connected spaces and homotopy theory of L∞ algebras

Buijs, Urtzi;Murillo, Aniceto
(2013) Advances in mathematics — Vol. 236, p. 60-91 (2013)

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Authors
  • Buijs, UrtziUCLouvain
    Author
  • Murillo, AnicetoDepartamento de Álgebra, Geometría y Topología, Universidad de Málaga, Málaga, Spain
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Abstract
We develop a homotopy theory of <inf>L∞</inf> algebras based on the Lawrence-Sullivan construction, a complete differential graded Lie algebra which, as we show, satisfies the necessary properties to become the right cylinder in this category. As a result, we obtain a general procedure to algebraically model the rational homotopy type of non-connected spaces. © 2012 Elsevier Ltd.
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Buijs, U., & Murillo, A. (2013). Algebraic models of non-connected spaces and homotopy theory of L∞ algebras. Advances in mathematics, 236, 60-91. https://doi.org/10.1016/j.aim.2012.12.014 (Original work published 2013)