Reference : Flat Z-graded connections and loop spaces
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Physical, chemical, mathematical & earth Sciences : Mathematics
Flat Z-graded connections and loop spaces
Arias Abad, Camilo [Universidad Nacional de Colombia en Medellín > Escuela de Matemáticas > > Profesor Asistente]
Schatz, Florian mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
[en] loop spaces ; iterated integrals ; dg modules
[en] The pull back of a flat bundle E→X along the evaluation map π:LX→X from the free loop space LX to X comes equipped with a canonical automorphism given by the holonomies of E. This construction naturally generalizes to flat Z-graded connections on X. Our main result is that the restriction of this holonomy automorphism to the based loop space ΩX of X provides an A-infinity quasi-equivalence between the dg category of flat Z-graded connections on X and the dg category of representations of C(ΩX), the dg algebra of singular chains on ΩX.
Swiss National Science Foundation ; Danish National Research Foundation by the center of excellence grant “Centre for Quantum Geometry of Moduli Spaces” (DNRF95)

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