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Derivations, the Lawrence–Sullivan interval and the Fiorenza–Manetti mapping cone

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We describe the rational homotopy type of any component of the based mapping space map*(X,Y) as an explicit L ∞ algebra defined on the (desuspended and positive) derivations between Quillen models of X and Y. When considering the Lawrence–Sullivan model of the interval, we obtain an L ∞ model of the contractible path space of Y. We then relate this, in a geometrical and natural manner, to the L ∞ structure on the Fiorenza–Manetti mapping cone of any differential graded Lie algebra morphism, two in principal different algebraic objects in which Bernoulli numbers appear.

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Authors and Affiliations

  1. Departament d’Àlgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes, 585, 08007, Barcelona, Spain

    Urtzi Buijs & Javier J. Gutiérrez

  2. Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, Ap. 59, 29080, Málaga, Spain

    Aniceto Murillo

Authors
  1. Urtzi Buijs
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  2. Javier J. Gutiérrez
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  3. Aniceto Murillo
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Correspondence to Aniceto Murillo.

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Dedicated to Yves Félix, on his 60th birthday

U. Buijs was supported by the MEC-FEDER grant MTM2010-15831 and a Juan de la Cierva research contract. J. J. Gutiérrez was supported by the MEC–FEDER grant MTM2010-15831 and by the Generalitat de Catalunya as a member of the team 2009 SGR 119. A. Murillo was supported by the MEC-FEDER grant MTM2010-18089 and the Junta de Andalucía grants FQM-213 and P07-FQM-2863.

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Buijs, U., Gutiérrez, J.J. & Murillo, A. Derivations, the Lawrence–Sullivan interval and the Fiorenza–Manetti mapping cone. Math. Z. 273, 981–997 (2013). https://doi.org/10.1007/s00209-012-1040-x

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  • DOI: https://doi.org/10.1007/s00209-012-1040-x

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