Reference : Higher holonomies: comparing two constructions

	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/22572

Title :	Higher holonomies: comparing two constructions
Language :	English
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 >]
Publication date :	2015
Journal title :	Differential Geometry and its Applications
Publisher :	Elsevier Science
Volume :	40
Pages :	14-42
Peer reviewed :	Yes (verified by ORBilu)
Audience :	International
ISSN :	0926-2245
City :	Amsterdam
Country :	The Netherlands
Keywords :	[en] higher holonomies ; superconnections ; Lie crossed modules
Abstract :	[en] We compare two different constructions of higher dimensional parallel transport. On the one hand, there is the two dimensional parallel transport associated to 2-connections on 2-bundles studied by Baez-Schreiber, Faria Martins-Picken and Schreiber-Waldorf. On the other hand, there are the higher holonomies associated to flat superconnections as studied by Igusa, Block-Smith and Arias Abad-Schätz. We first explain how by truncating the latter construction one obtains examples of the former. Then we prove that the 2-dimensional holonomies provided by the two approaches coincide.
Research centres :	Centre for Quantum Geometry of Moduli Spaces, Aarhus University (Aarhus, Denmark)
Funders :	Swiss National Science Foundation (SNF Grant 200020-131813/1) ; Humboldt Foundation (Germany) ; Danish National Research Foundation by grant DNRF95 (Centre for Quantum Geometry of Moduli Spaces - QGM) ; Centre for Quantum Geometry of Moduli Spaces, Aarhus University (Aarhus, Denmark)
Target :	Researchers
Permalink :	http://hdl.handle.net/10993/22572
DOI :	10.1016/j.difgeo.2015.02.003
Other URL :	http://www.sciencedirect.com/science/article/pii/S0926224515000236
Mentions required by the publisher for OA :	The original publication is available at http://www.sciencedirect.com/science/article/pii/S0926224515000236

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