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


Alexander Berglund (Department of Mathematics, Stockholm University, Stockholm, Sweden)


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.


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

2010 Mathematics Subject Classification

55P62, 55U10

Published 3 December 2015