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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