Tate-valued Characteristic Classes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915199868469248 |
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| author | Carmeli, Shachar Luecke, Kiran |
| author_facet | Carmeli, Shachar Luecke, Kiran |
| contents | We define a projective variant of classical complex orientation theory. Using this, we construct a map of spectra which lifts the total Chern class, providing an alternative answer to an old question of Segal \cite{segal}, previously answered by Lawson et al \cite{lawsonetal}. We also lift and generalize the ``sharp'' construction of Ando-French-Ganter \cite{afg} to an operation on arbitrary $\EE_\infty$-complex orientations, thereby providing a rich source of new $\EE_\infty$-orientations for commutative ring spectra. In particular we give an $\EE_\infty$-lift of the Jacobi orientation, a generalization of the much-studied two variable elliptic genus. Finally, we construct some new complex orientations of periodic ring spectra as requested in \cite{hahnyuan}. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_12134 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tate-valued Characteristic Classes Carmeli, Shachar Luecke, Kiran Algebraic Topology 55R40, 55R77 We define a projective variant of classical complex orientation theory. Using this, we construct a map of spectra which lifts the total Chern class, providing an alternative answer to an old question of Segal \cite{segal}, previously answered by Lawson et al \cite{lawsonetal}. We also lift and generalize the ``sharp'' construction of Ando-French-Ganter \cite{afg} to an operation on arbitrary $\EE_\infty$-complex orientations, thereby providing a rich source of new $\EE_\infty$-orientations for commutative ring spectra. In particular we give an $\EE_\infty$-lift of the Jacobi orientation, a generalization of the much-studied two variable elliptic genus. Finally, we construct some new complex orientations of periodic ring spectra as requested in \cite{hahnyuan}. |
| title | Tate-valued Characteristic Classes |
| topic | Algebraic Topology 55R40, 55R77 |
| url | https://arxiv.org/abs/2503.12134 |