Bochner-type theorems for distributional category
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918343412285440 |
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| author | Jauhari, Ekansh Oprea, John |
| author_facet | Jauhari, Ekansh Oprea, John |
| contents | We show that in the presence of a geometric condition such as non-negative Ricci curvature, the distributional category of a manifold may be used to bound invariants, such as the first Betti number and macroscopic dimension, from above. Moreover, à la Bochner, when the bound is an equality, special constraints are imposed on the manifold. We show that the distributional category of a space also bounds the rank of the Gottlieb group, with equality imposing constraints on the fundamental group. These bounds are refined in the setting of cohomologically symplectic manifolds, enabling us to get specific computations for the distributional category and LS-category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21763 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bochner-type theorems for distributional category Jauhari, Ekansh Oprea, John Algebraic Topology Group Theory Geometric Topology 57N65 (Primary) 55M30, 20J06, 53C23 (Secondary) We show that in the presence of a geometric condition such as non-negative Ricci curvature, the distributional category of a manifold may be used to bound invariants, such as the first Betti number and macroscopic dimension, from above. Moreover, à la Bochner, when the bound is an equality, special constraints are imposed on the manifold. We show that the distributional category of a space also bounds the rank of the Gottlieb group, with equality imposing constraints on the fundamental group. These bounds are refined in the setting of cohomologically symplectic manifolds, enabling us to get specific computations for the distributional category and LS-category. |
| title | Bochner-type theorems for distributional category |
| topic | Algebraic Topology Group Theory Geometric Topology 57N65 (Primary) 55M30, 20J06, 53C23 (Secondary) |
| url | https://arxiv.org/abs/2505.21763 |