## Holonomies for connections with values in L_infty algebras

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• Camilo Arias Abad, Max-Planck Institut für Mathematik, Bonn, Germany
• Florian Schaetz, Denmark
Given a flat connection $\alpha$ on a manifold $M$ with values in a filtered $L_\infty$-algebra $g$, we construct a morphism $hol^\infty_\alpha: C(M) B\hat{U}_\infty(g)$, generalizing the holonomies of
flat connections with values in Lie algebras. The construction is based on Gugenheim's $A_\infty$-version of de Rham's theorem, which in turn is based on Chen's iterated integrals.
Original language English Homology, Homotopy and Applications 16 1 89-118 30 1532-0073 https://doi.org/10.4310/HHA.2014.v16.n1.a6 Published - 2014

### Research areas

• L_infty algebras, configuration space, braid group, iterated integrals, higher holonomies

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ID: 73625051