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.
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)
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