Rational homotopy theory of mapping spaces via Lie theory for L-infinity algebras

Details Rational homotopy theory of mapping spaces via Lie theory for L-infinity algebras Rational homotopy theory of mapping spaces via Lie theory for L-infinity algebras

2011-10-27

arxiv.org/abs/1110.6145v1

Mathematics

Algebraic Topology

21 pages

Scientific paper

We calculate the higher homotopy groups of the Deligne-Getzler infinity-groupoid associated to an L-infinity algebra and we describe Sullivan models for its connected components. As an application, we present a new approach to the rational homotopy theory of mapping spaces. For a connected space X and a nilpotent space Y of finite type, the mapping space Map(X,Y_Q) is homotopy equivalent to the infinity-groupoid associated to the completed tensor product of A and L, where A is a commutative differential graded algebra model for X and L is an L-infinity algebra model for Y. This enables us to calculate Sullivan models for the components of Map(X,Y_Q).

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