Functoriality for higher rho invariants of elliptic operators
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866916374885957632 |
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| author | Guo, Hao Xie, Zhizhang Yu, Guoliang |
| author_facet | Guo, Hao Xie, Zhizhang Yu, Guoliang |
| contents | Let $N$ be a closed spin manifold with positive scalar curvature and $D_N$ the Dirac operator on $N$. Let $M_1$ and $M_2$ be two Galois covers of $N$ such that $M_2$ is a quotient of $M_1$. Then the quotient map from $M_1$ to $M_2$ naturally induces maps between the geometric $C^*$-algebras associated to the two manifolds. We prove, by a finite-propagation argument, that the \emph{maximal} higher rho invariants of the lifts of $D_N$ to $M_1$ and $M_2$ behave functorially with respect to the above quotient map. This can be applied to the computation of higher rho invariants, along with other related invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_01933 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Functoriality for higher rho invariants of elliptic operators Guo, Hao Xie, Zhizhang Yu, Guoliang K-Theory and Homology Differential Geometry Operator Algebras 46L80, 58B34, 53C20 Let $N$ be a closed spin manifold with positive scalar curvature and $D_N$ the Dirac operator on $N$. Let $M_1$ and $M_2$ be two Galois covers of $N$ such that $M_2$ is a quotient of $M_1$. Then the quotient map from $M_1$ to $M_2$ naturally induces maps between the geometric $C^*$-algebras associated to the two manifolds. We prove, by a finite-propagation argument, that the \emph{maximal} higher rho invariants of the lifts of $D_N$ to $M_1$ and $M_2$ behave functorially with respect to the above quotient map. This can be applied to the computation of higher rho invariants, along with other related invariants. |
| title | Functoriality for higher rho invariants of elliptic operators |
| topic | K-Theory and Homology Differential Geometry Operator Algebras 46L80, 58B34, 53C20 |
| url | https://arxiv.org/abs/2005.01933 |