A Lichnerowicz Vanishing Theorem for the Maximal Roe Algebra
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866929478769311744 |
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| author | Guo, Hao Xie, Zhizhang Yu, Guoliang |
| author_facet | Guo, Hao Xie, Zhizhang Yu, Guoliang |
| contents | We show that if a countable discrete group acts properly and isometrically on a spin manifold of bounded Riemannian geometry and uniformly positive scalar curvature, then, under a suitable condition on the group action, the maximal higher index of the Dirac operator vanishes in K-theory of the maximal equivariant Roe algebra. The group action is not assumed to be cocompact. A key step in the proof is to establish a functional calculus for the Dirac operator in the maximal equivariant uniform Roe algebra. This allows us to prove vanishing of the index of the Dirac operator in K-theory of this algebra, which in turn yields the result for the maximal higher index. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_12299 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A Lichnerowicz Vanishing Theorem for the Maximal Roe Algebra Guo, Hao Xie, Zhizhang Yu, Guoliang K-Theory and Homology Differential Geometry Operator Algebras 46L80, 53C20, 58B34 We show that if a countable discrete group acts properly and isometrically on a spin manifold of bounded Riemannian geometry and uniformly positive scalar curvature, then, under a suitable condition on the group action, the maximal higher index of the Dirac operator vanishes in K-theory of the maximal equivariant Roe algebra. The group action is not assumed to be cocompact. A key step in the proof is to establish a functional calculus for the Dirac operator in the maximal equivariant uniform Roe algebra. This allows us to prove vanishing of the index of the Dirac operator in K-theory of this algebra, which in turn yields the result for the maximal higher index. |
| title | A Lichnerowicz Vanishing Theorem for the Maximal Roe Algebra |
| topic | K-Theory and Homology Differential Geometry Operator Algebras 46L80, 53C20, 58B34 |
| url | https://arxiv.org/abs/1905.12299 |