Higher holonomies: comparing two constructions
Algebraic Topology
2014-04-04 v1
Abstract
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-Schaetz. 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.
Cite
@article{arxiv.1404.0729,
title = {Higher holonomies: comparing two constructions},
author = {Camilo Arias Abad and Florian Schaetz},
journal= {arXiv preprint arXiv:1404.0729},
year = {2014}
}
Comments
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