On Systole, Kissing Number and Volume of Arithmetic Manifolds
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910173529899008 |
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| author | Murillo, Plinio Guillel Pino |
| author_facet | Murillo, Plinio Guillel Pino |
| contents | The purpose of this expository article is to give a down-to-hearth introduction to the notion of an arithmetic group and arithmetic manifold. To achieve this we have decided to bring two geometrical questions relating the growth of systole and kissing number in hyperbolic manifolds, as a motivational guide, whose answers so far are given by the use of arithmetic manifolds. As a consequence, we answer these questions in detail for dimension 2, we mention was is known for hyperbolic manifolds of higher dimension, and also for other locally symmetric spaces. We end the exposition with some open questions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_00857 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Systole, Kissing Number and Volume of Arithmetic Manifolds Murillo, Plinio Guillel Pino Geometric Topology 53C22, 11F06, 11R52, 32Q05 The purpose of this expository article is to give a down-to-hearth introduction to the notion of an arithmetic group and arithmetic manifold. To achieve this we have decided to bring two geometrical questions relating the growth of systole and kissing number in hyperbolic manifolds, as a motivational guide, whose answers so far are given by the use of arithmetic manifolds. As a consequence, we answer these questions in detail for dimension 2, we mention was is known for hyperbolic manifolds of higher dimension, and also for other locally symmetric spaces. We end the exposition with some open questions. |
| title | On Systole, Kissing Number and Volume of Arithmetic Manifolds |
| topic | Geometric Topology 53C22, 11F06, 11R52, 32Q05 |
| url | https://arxiv.org/abs/2509.00857 |