A note on discrete Holonomy through directed edges, with no lengths

Stuart Armstrong; Jussi Westergren

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arXiv · 0902.2301

A note on discrete Holonomy through directed edges, with no lengths

Stuart Armstrong·Jussi Westergren

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Abstract

This note demonstrates how both the concept of distance and the concept of holonomy can be constructed from a suitable network with directed edges (and no lengths). The number of different edge types depends on the signature of the metric and the dimension of the holonomy group. If the holonomy group is of dimension one and the metric is positive-definite, a single type of directed edges is needed.

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Stuart Armstrong, Jussi Westergren. 2009-02-13. A note on discrete Holonomy through directed edges, with no lengths. https://arxiv.org/abs/0902.2301

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