Reference : Holonomies for connections with values in L_infty algebras
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Holonomies for connections with values in L_infty algebras
Arias Abad, Camilo [Universidad Nacional de Colombia en Medellín (Colombia) > Escuela de Matemáticas > > Profesor Asistente]
Schatz, Florian mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Homology, Homotopy and Applications
International Press of Boston
Yes (verified by ORBilu)
[en] higher holonomies ; rational homotopy theory ; flat superconnections
[en] Given a flat connection on a manifold M with values in a filtered L-infinity-algebra g, we construct a morphism, generalizing the holonomies of flat connections with values in Lie algebras. The construction is based on Gugenheim's A-infinity 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 Rd, and to generalizations of the holonomy representations of braid groups.
Centre for Quantum Geometry of Moduli Spaces, Aarhus University (Aarhus, Denmark)
Swiss National Science Foundation (SNF-grant 200020-131813/1) ; Humboldt Stiftung (Germany) ; ERC Starting Grant no. 279729 ; Danish National Research Foundation grant DNRF95 (Centre for Quantum Geometry of Moduli Spaces - QGM) ; Utrecht University (Utrecht, The Netherlands)
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