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arXiv · 1404.0729

Higher holonomies: comparing two constructions

Camilo Arias Abad·Florian Schaetz
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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.

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Camilo Arias Abad, Florian Schaetz. 2014-04-02. Higher holonomies: comparing two constructions. https://arxiv.org/abs/1404.0729

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