A fixed-point formula for Dirac operators on Lie groupoids
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866911964070936576 |
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| author | Sadegh, Ahmad Reza Haj Saeedi Liu, Shiqi Loizides, Yiannis Sanchez, Jesus |
| author_facet | Sadegh, Ahmad Reza Haj Saeedi Liu, Shiqi Loizides, Yiannis Sanchez, Jesus |
| contents | We study equivariant families of Dirac operators on the source fibers of a Lie groupoid with a closed space of units and equipped with an action of an auxiliary compact Lie group. We use the Getzler rescaling method to derive a fixed-point formula for the pairing of a trace with the K-theory class of such a family. For the pair groupoid of a closed manifold, our formula reduces to the standard fixed-point formula for the equivariant index of a Dirac operator. Further examples involve foliations and manifolds equipped with a normal crossing divisor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_11061 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A fixed-point formula for Dirac operators on Lie groupoids Sadegh, Ahmad Reza Haj Saeedi Liu, Shiqi Loizides, Yiannis Sanchez, Jesus Differential Geometry K-Theory and Homology We study equivariant families of Dirac operators on the source fibers of a Lie groupoid with a closed space of units and equipped with an action of an auxiliary compact Lie group. We use the Getzler rescaling method to derive a fixed-point formula for the pairing of a trace with the K-theory class of such a family. For the pair groupoid of a closed manifold, our formula reduces to the standard fixed-point formula for the equivariant index of a Dirac operator. Further examples involve foliations and manifolds equipped with a normal crossing divisor. |
| title | A fixed-point formula for Dirac operators on Lie groupoids |
| topic | Differential Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2307.11061 |