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Title of Journal: Math Z

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Abbravation: Mathematische Zeitschrift

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Springer-Verlag

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DOI

10.1002/cncr.11651

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1432-1823

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Derivations the Lawrence–Sullivan interval and th

Authors: Urtzi Buijs Javier J Gutiérrez Aniceto Murillo
Publish Date: 2012/06/10
Volume: 273, Issue: 3-4, Pages: 981-997
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Abstract

We describe the rational homotopy type of any component of the based mapping space mapXY 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 appearU Buijs was supported by the MECFEDER grant MTM201015831 and a Juan de la Cierva research contract J J Gutiérrez was supported by the MEC–FEDER grant MTM201015831 and by the Generalitat de Catalunya as a member of the team 2009 SGR 119 A Murillo was supported by the MECFEDER grant MTM201018089 and the Junta de Andalucía grants FQM213 and P07FQM2863

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