Reference : The A_infty de Rham theorem and integration of representations up to homotopy
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/22561
The A_infty de Rham theorem and integration of representations up to homotopy
English
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 >]
2013
International Mathematics Research Notices
Oxford University Press
2013
16
3790-3855
Yes (verified by ORBilu)
International
1073-7928
1687-0247
Oxford
United Kingdom
[en] representations up to homotopy ; Lie algebroids ; higher holonomies
[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.
Center for Mathematical Analysis, Geometry and Dynamical Systems, IST Lisbon (Lisbon, Portugal)
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
Researchers
http://hdl.handle.net/10993/22561
10.1093/imrn/rns166
http://imrn.oxfordjournals.org/content/2013/16/3790.full?sid=9e340d93-3d2a-40fa-8898-88bea12b9171
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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