Bounding the A-hat genus using scalar curvature lower bounds and isoperimetric constants
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910645456207872 |
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| author | Ma, Qiaochu Wang, Jinmin Yu, Guoliang Zhu, Bo |
| author_facet | Ma, Qiaochu Wang, Jinmin Yu, Guoliang Zhu, Bo |
| contents | In this paper, we prove an upper bound on the $\widehat{A}$ genus of a smooth, closed, spin Riemannian manifold using its scalar curvature lower bound, Neumann isoperimetric constant, and volume. The proof of this result relies on spectral analysis of the Dirac operator. We also construct an example to show that the Neumann isoperimetric constant in this bound is necessary. Our result partially answers a question of Gromov on bounding characteristic numbers using scalar curvature lower bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08866 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bounding the A-hat genus using scalar curvature lower bounds and isoperimetric constants Ma, Qiaochu Wang, Jinmin Yu, Guoliang Zhu, Bo Differential Geometry Analysis of PDEs Algebraic Topology K-Theory and Homology In this paper, we prove an upper bound on the $\widehat{A}$ genus of a smooth, closed, spin Riemannian manifold using its scalar curvature lower bound, Neumann isoperimetric constant, and volume. The proof of this result relies on spectral analysis of the Dirac operator. We also construct an example to show that the Neumann isoperimetric constant in this bound is necessary. Our result partially answers a question of Gromov on bounding characteristic numbers using scalar curvature lower bound. |
| title | Bounding the A-hat genus using scalar curvature lower bounds and isoperimetric constants |
| topic | Differential Geometry Analysis of PDEs Algebraic Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2410.08866 |