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The A∞ de Rham theorem and integration of representations up to homotopy


Arias Abad, Camilo; Schätz, Florian (2013). The A∞ de Rham theorem and integration of representations up to homotopy. International Mathematics Research Notices, 2013(16):3790-3855.

Abstract

We use Chen's iterated integrals to integrate representations up to homotopy. That is, we construct an 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 version of de Rham's theorem due to Gugenheim [15]. The integration procedure we explain here amounts to extending the construction of parallel transport for superconnections, introduced by Igusa [17] and Block-Smith [6], to the case of certain differential graded manifolds

Abstract

We use Chen's iterated integrals to integrate representations up to homotopy. That is, we construct an 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 version of de Rham's theorem due to Gugenheim [15]. The integration procedure we explain here amounts to extending the construction of parallel transport for superconnections, introduced by Igusa [17] and Block-Smith [6], to the case of certain differential graded manifolds

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:National licences > 142-005
Dewey Decimal Classification:Unspecified
Scopus Subject Areas:Physical Sciences > General Mathematics
Language:English
Date:1 January 2013
Deposited On:02 Nov 2018 16:27
Last Modified:15 Apr 2021 14:50
Publisher:Oxford University Press
ISSN:1073-7928
OA Status:Green
Publisher DOI:https://doi.org/10.1093/imrn/rns166

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