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arXiv · 2002.09775

The derivative of global surface-holonomy for a non-abelian gerbe

Cheyne J Glass
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Abstract

Starting with a non-abelian gerbe represented by a non-abelian differential cocycle, with values in a given crossed-module, this paper explicitly calculates a formula for the derivative of the associated surface holonomy of squares mapped into the base manifold; with spheres later considered as a special case. While the definitions in this paper used for gerbes, their connections, and the induced holonomy will initially be simplicial, translations into a cubical setting will be provided to aide in explicit coordinate-based calculations. While there are many previously published results on the properties of these non-abelian gerbes, including some calculations of the derivative over a single open set, this paper endeavors to take these local calculations and glue them together across multiple open sets in order to obtain a single expression for the change in surface holonomy with respect to a one-parameter family of squares.

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Cheyne J Glass. 2020-02-22. The derivative of global surface-holonomy for a non-abelian gerbe. https://doi.org/10.1016/j.difgeo.2021.101737

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