^{1} Department of Mathematics - Centre for Quantum Geometry of Moduli Spaces, Department of Mathematics, Science and Technology, Aarhus University^{2} Max-Planck Institut für Mathematik, Bonn^{3} Department of Mathematics - Centre for Quantum Geometry of Moduli Spaces, Department of Mathematics, Science and Technology, Aarhus University

DOI:

10.4310/HHA.2014.v16.n1.a6

Abstract:

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.

Type:

Journal article

Language:

English

Published in:

Homology, Homotopy and Applications, 2014, Vol 16, Issue 1, p. 89-118