Abelian subgroups of the fundamental group of a space with no conjugate points
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866913804624855040 |
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| author | Dibble, James |
| author_facet | Dibble, James |
| contents | Each Abelian subgroup of the fundamental group of a compact and locally simply connected $d$-dimensional length space with no conjugate points is isomorphic to $\mathbb{Z}^k$ for some $0 \leq k \leq d$. It follows from this and previously known results that each solvable subgroup of the fundamental group is a Bieberbach group. In the Riemannian setting, this may be proved using a novel property of the asymptotic norm of each Abelian subgroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_10095 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Abelian subgroups of the fundamental group of a space with no conjugate points Dibble, James Differential Geometry 20F65, 53C20 (Primary), 53C22 (Secondary) Each Abelian subgroup of the fundamental group of a compact and locally simply connected $d$-dimensional length space with no conjugate points is isomorphic to $\mathbb{Z}^k$ for some $0 \leq k \leq d$. It follows from this and previously known results that each solvable subgroup of the fundamental group is a Bieberbach group. In the Riemannian setting, this may be proved using a novel property of the asymptotic norm of each Abelian subgroup. |
| title | Abelian subgroups of the fundamental group of a space with no conjugate points |
| topic | Differential Geometry 20F65, 53C20 (Primary), 53C22 (Secondary) |
| url | https://arxiv.org/abs/1811.10095 |