An index formula for families of end-periodic Dirac operators
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909729396097024 |
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| author | Taylor, Alex R. |
| author_facet | Taylor, Alex R. |
| contents | We derive a transgression formula for the renormalized Chern character of the Bismut superconnection in the context of end-periodic fiber bundles and families of end-periodic Clifford modules. The transgression is expressed in terms of the Fourier-Laplace transform of the Bismut superconnection using the renormalized supertrace of Mrowka-Ruberman-Saveliev. Consequently, we establish an index formula for families of Dirac operators on end-periodic manifolds. The index formula involves a new ``end-periodic eta form'' which generalizes both the Bismut-Cheeger eta form and the end-periodic eta invariant of Mrowka-Ruberman-Saveliev. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06029 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An index formula for families of end-periodic Dirac operators Taylor, Alex R. Differential Geometry Analysis of PDEs Geometric Topology 58J20, 58J28, 58J35, 35K05, 19K56 We derive a transgression formula for the renormalized Chern character of the Bismut superconnection in the context of end-periodic fiber bundles and families of end-periodic Clifford modules. The transgression is expressed in terms of the Fourier-Laplace transform of the Bismut superconnection using the renormalized supertrace of Mrowka-Ruberman-Saveliev. Consequently, we establish an index formula for families of Dirac operators on end-periodic manifolds. The index formula involves a new ``end-periodic eta form'' which generalizes both the Bismut-Cheeger eta form and the end-periodic eta invariant of Mrowka-Ruberman-Saveliev. |
| title | An index formula for families of end-periodic Dirac operators |
| topic | Differential Geometry Analysis of PDEs Geometric Topology 58J20, 58J28, 58J35, 35K05, 19K56 |
| url | https://arxiv.org/abs/2508.06029 |