Reference : Higher holonomies: comparing two constructions
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Higher holonomies: comparing two constructions
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 >]
Differential Geometry and its Applications
Elsevier Science
Yes (verified by ORBilu)
The Netherlands
[en] higher holonomies ; superconnections ; Lie crossed modules
[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.
Centre for Quantum Geometry of Moduli Spaces, Aarhus University (Aarhus, Denmark)
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)
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