Connected holonomy is lower semicontinuous
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866914166688710656 |
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| author | Müller, Olaf |
| author_facet | Müller, Olaf |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_05572 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Connected holonomy is lower semicontinuous Müller, Olaf Differential Geometry 53C29 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. |
| title | Connected holonomy is lower semicontinuous |
| topic | Differential Geometry 53C29 |
| url | https://arxiv.org/abs/2109.05572 |