Covering complexity, scalar curvature, and quantitative $K$-theory
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929478816497664 |
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| author | Guo, Hao Yu, Guoliang |
| author_facet | Guo, Hao Yu, Guoliang |
| contents | We establish a relationship between a certain notion of covering complexity of a Riemannian spin manifold and positive lower bounds on its scalar curvature. This makes use of a pairing between quantitative operator $K$-theory and Lipschitz topological $K$-theory, combined with an earlier vanishing theorem for the quantitative higher index. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_15003 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Covering complexity, scalar curvature, and quantitative $K$-theory Guo, Hao Yu, Guoliang K-Theory and Homology Differential Geometry Operator Algebras 46L80, 58B34, 53C20 We establish a relationship between a certain notion of covering complexity of a Riemannian spin manifold and positive lower bounds on its scalar curvature. This makes use of a pairing between quantitative operator $K$-theory and Lipschitz topological $K$-theory, combined with an earlier vanishing theorem for the quantitative higher index. |
| title | Covering complexity, scalar curvature, and quantitative $K$-theory |
| topic | K-Theory and Homology Differential Geometry Operator Algebras 46L80, 58B34, 53C20 |
| url | https://arxiv.org/abs/2203.15003 |