Work

Holonomies for connections with values in $L_\infty$-algebras

Year: 2014

Type: article

Abstract: Given a flat connection α on a manifold M with values in a filtered L ∞ -algebra g, we construct a morphism hol ∞ α : C • (M ) → B Û∞ (g), which generalizes the holonomy map associated to a flat connection with values in a Lie algebra.The construction is based on Gugenheim's A ∞ -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 R d , and to generalizations of the holonomy representations of braid groups. C.A.A.

Source: Homology Homotopy and Applications

DOI: 10.4310/hha.2014.v16.n1.a6

Authors: Camilo Arias Abad, Florian Schätz

Institutions: Max Planck Institute for Mathematics, Aarhus University

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze