Growth of k-dimensional systoles in congruence coverings
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911860877426688 |
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| author | Belolipetsky, Mikhail Weinberger, Shmuel |
| author_facet | Belolipetsky, Mikhail Weinberger, Shmuel |
| contents | We study growth of absolute and homological $k$-dimensional systoles of arithmetic $n$-manifolds along congruence coverings. Our main interest is in the growth of systoles of manifolds whose real rank $r > 1$. We observe, in particular, that in some cases for $k = r$ the growth function tends to oscillate between a power of a logarithm and a power function of the degree of the covering. This is a new phenomenon. We also prove the expected polylogarithmic and constant power bounds for small and large $k$, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_03196 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Growth of k-dimensional systoles in congruence coverings Belolipetsky, Mikhail Weinberger, Shmuel Geometric Topology Group Theory We study growth of absolute and homological $k$-dimensional systoles of arithmetic $n$-manifolds along congruence coverings. Our main interest is in the growth of systoles of manifolds whose real rank $r > 1$. We observe, in particular, that in some cases for $k = r$ the growth function tends to oscillate between a power of a logarithm and a power function of the degree of the covering. This is a new phenomenon. We also prove the expected polylogarithmic and constant power bounds for small and large $k$, respectively. |
| title | Growth of k-dimensional systoles in congruence coverings |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2302.03196 |