Connected holonomy is lower semicontinuous

Olaf Müller

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arXiv · 2109.05572

Connected holonomy is lower semicontinuous

Olaf Müller

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Abstract

In this article, we examine continuity properties of the maps $|Hol$ and $\Hol^0$ assigning, on a fixed manifold $M$, to a metric on $M$ its holonomy class resp. restricted holonomy class (conjugacy class of the connected component of the holonomy representation). Among related results, we show that $\Hol^0$ is lower semicontinuous w.r.t. $C^1$ topology on the space of $C^2$ metrics.

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Olaf Müller. 2021-09-12. Connected holonomy is lower semicontinuous. https://arxiv.org/abs/2109.05572

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