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

作者：Buijs Urtzi; Gutierrez Javier J; Murillo Aniceto^*

来源：Mathematische Zeitschrift, 2013, 273(3-4): 981-997.

DOI：10.1007/s00209-012-1040-x

• Rational homotopy
• Mapping space
• L infinity-algebras

We describe the rational homotopy type of any component of the based mapping space map(*)(X,Y) as an explicit L (a) 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 (a) model of the contractible path space of Y. We then relate this, in a geometrical and natural manner, to the L (a) 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.

• 出版日期2013-4