Abstract
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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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