Small scale index theory, scalar curvature, and Gromov's simplicial norms
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915594400432128 |
|---|---|
| author | Ma, Qiaochu Yu, Guoliang |
| author_facet | Ma, Qiaochu Yu, Guoliang |
| contents | In this article, we study the topological complexity of manifolds with a lower scalar curvature bound. We introduce a small scale index theorem to establish an upper bound for Gromov's simplicial norm of the Poincaré dual of the A-hat class for manifolds with spin universal covering, in terms of a scalar curvature lower bound, volume upper bound, and injectivity radius lower bound of the universal covering. This result can be viewed both as a generalization of Lichnerowicz vanishing theorem and as a scalar curvature analogue to Cheeger finiteness theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14791 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Small scale index theory, scalar curvature, and Gromov's simplicial norms Ma, Qiaochu Yu, Guoliang Differential Geometry Geometric Topology K-Theory and Homology In this article, we study the topological complexity of manifolds with a lower scalar curvature bound. We introduce a small scale index theorem to establish an upper bound for Gromov's simplicial norm of the Poincaré dual of the A-hat class for manifolds with spin universal covering, in terms of a scalar curvature lower bound, volume upper bound, and injectivity radius lower bound of the universal covering. This result can be viewed both as a generalization of Lichnerowicz vanishing theorem and as a scalar curvature analogue to Cheeger finiteness theorem. |
| title | Small scale index theory, scalar curvature, and Gromov's simplicial norms |
| topic | Differential Geometry Geometric Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2508.14791 |