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Flat Z-graded connections and loop spaces
Arias Abad, Camilo; SCHATZ, Florian
2015
 

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Keywords :
loop spaces; iterated integrals; dg modules
Abstract :
[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.
Disciplines :
Mathematics
Author, co-author :
Arias Abad, Camilo;  Universidad Nacional de Colombia en Medellín > Escuela de Matemáticas > Profesor Asistente
SCHATZ, Florian ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
Flat Z-graded connections and loop spaces
Publication date :
2015
Number of pages :
35
Funders :
SNSF - Swiss National Science Foundation [CH]
Danish National Research Foundation by the center of excellence grant “Centre for Quantum Geometry of Moduli Spaces” (DNRF95)
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since 25 November 2015

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