Geodesic
Holonomies for connections with values in $L_{\infty}$-algebras
Homology, homotopy, and applications, Tome 16 (2014) no. 1, pp. 89-118.

Voir la notice de l'article provenant de la source International Press of Boston

Given a flat connection $\alpha$ on a manifold $M$ with values in a filtered $L_\infty$-algebra $\mathfrak{g}$, we construct a morphism $\mathsf{hol}^{\infty}_\alpha \colon C_\bullet(M) \rightarrow \mathsf{B} \hat{\mathbb{U}}_\infty(\mathfrak{g})$, which generalizes the holonomy map associated to a flat connection with values in a Lie algebra. The construction is based on Gugenheim’s $\mathsf{A}_{\infty}$-version of de Rham’s theorem, which in turn is based on Chen’s iterated integrals. Finally, we discuss examples related to the geometry of configuration spaces of points in Euclidean space $\mathbb{R}^d$, and to generalizations of the holonomy representations of braid groups. 
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     author = {Camilo Arias Abad and Florian Sch\"atz},
     title = {Holonomies for connections with values in $L_{\infty}$-algebras},
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     pages = {89--118},
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     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2014.v16.n1.a6/}
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Camilo Arias Abad; Florian Schätz. Holonomies for connections with values in $L_{\infty}$-algebras. Homology, homotopy, and applications, Tome 16 (2014) no. 1, pp. 89-118. doi : 10.4310/HHA.2014.v16.n1.a6. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2014.v16.n1.a6/

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