Article (Scientific journals)
The A_infty de Rham theorem and integration of representations up to homotopy
Arias Abad, Camilo; Schatz, Florian
2013In International Mathematics Research Notices, 2013 (16), p. 3790-3855
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The original publication is available at http://imrn.oxfordjournals.org/content/2013/16/3790.full?sid=9e340d93-3d2a-40fa-8898-88bea12b9171


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Keywords :
representations up to homotopy; Lie algebroids; higher holonomies
Abstract :
[en] We use Chen's iterated integrals to integrate representations up to homotopy. That is, we construct an A-infinity functor from the representations up to homotopy of a Lie algebroid A to those of its infinity groupoid. This construction extends the usual integration of representations in Lie theory. We discuss several examples including Lie algebras and Poisson manifolds. The construction is based on an A-infinity version of de Rham's theorem due to Gugenheim. The integration procedure we explain here amounts to extending the construction of parallel transport for superconnections, introduced by Igusa and Block-Smith, to the case of certain differential graded manifolds.
Research center :
Center for Mathematical Analysis, Geometry and Dynamical Systems, IST Lisbon (Lisbon, Portugal)
Disciplines :
Mathematics
Author, co-author :
Arias Abad, Camilo;  Universidad Nacional de Colombia en Medellín (Colombia) > Escuela de Matemáticas > Profesor Asistente
Schatz, Florian ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
yes
Language :
English
Title :
The A_infty de Rham theorem and integration of representations up to homotopy
Publication date :
2013
Journal title :
International Mathematics Research Notices
ISSN :
1687-0247
Publisher :
Oxford University Press, Oxford, United Kingdom
Volume :
2013
Issue :
16
Pages :
3790-3855
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
Swiss National Science Foundation (SNF-grant 200020-121640/1)
Erwin Schrödinger Institute (Vienna, Austria)
Center for Mathematical Analysis, Geometry and Dynamical Systems, IST Lisbon (Lisbon, Portugal)
FCT/POCTI/FEDER through project PTDC/MAT/098936/2008
FCT postdoc grant SFRH/BPD/69197/2010
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