An extended variational formula for the Bismut-Cheeger eta form and its applications
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866910282703437824 |
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| author | Ho, Man-Ho |
| author_facet | Ho, Man-Ho |
| contents | The purpose of this paper is to extend our previous work on the variational formula for the Bismut-Cheeger eta form without the kernel bundle assumption by allowing the spin$^c$ Dirac operators to be twisted by isomorphic vector bundles, and to establish the $\mathbb{Z}_2$-graded additivity of the Bismut-Cheeger eta form. Using these results, we give alternative proofs of the fact that the analytic index in differential $K$-theory is a well defined group homomorphism, and the Riemann-Roch-Grothendieck theorem in $\mathbb{R}/\mathbb{Z}$ $K$-theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_00502 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An extended variational formula for the Bismut-Cheeger eta form and its applications Ho, Man-Ho K-Theory and Homology Differential Geometry 19K56, 19L50, 19L10 The purpose of this paper is to extend our previous work on the variational formula for the Bismut-Cheeger eta form without the kernel bundle assumption by allowing the spin$^c$ Dirac operators to be twisted by isomorphic vector bundles, and to establish the $\mathbb{Z}_2$-graded additivity of the Bismut-Cheeger eta form. Using these results, we give alternative proofs of the fact that the analytic index in differential $K$-theory is a well defined group homomorphism, and the Riemann-Roch-Grothendieck theorem in $\mathbb{R}/\mathbb{Z}$ $K$-theory. |
| title | An extended variational formula for the Bismut-Cheeger eta form and its applications |
| topic | K-Theory and Homology Differential Geometry 19K56, 19L50, 19L10 |
| url | https://arxiv.org/abs/2209.00502 |