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# Homology, Homotopy and Applications

## Volume 17 (2015)

### Number 2

### Rational homotopy theory of mapping spaces via Lie theory for $L_\infty$-algebras

Pages: 343 – 369

DOI: http://dx.doi.org/10.4310/HHA.2015.v17.n2.a16

#### Author

#### Abstract

We calculate the higher homotopy groups of the Deligne–Getzler $\infty$-groupoid associated to a nilpotent $L_\infty$-algebra. As an application, we present a new approach to the rational homotopy theory of mapping spaces.

#### Keywords

L-infinity algebra, Deligne groupoid, rational homotopy theory, mapping space

#### 2010 Mathematics Subject Classification

55P62, 55U10