Tate-valued Characteristic Classes II: Applications
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917002736566272 |
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| author | Carmeli, Shachar Luecke, Kiran |
| author_facet | Carmeli, Shachar Luecke, Kiran |
| contents | We present a construction that manufactures $\E_\infty$ orientations of Tate fixed-point objects together with useful formulas for these maps, and then give a number of applications. For example, we produce a formula for the Frobenius homomorphisms of Thom spectra such as $\MU$ as well as certain lifts of Frobenius. We prove a rigidity property of $\MU$ as a \emph{cyclotomic} object. We construct a general obstruction theory for $\E_n$ complex orientations and establish various non-existence results for $p$-typical $\E_n$ orientations for low values of $p$ and $n$. We end with some miscellaneous further applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01488 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tate-valued Characteristic Classes II: Applications Carmeli, Shachar Luecke, Kiran Algebraic Topology 55R40 We present a construction that manufactures $\E_\infty$ orientations of Tate fixed-point objects together with useful formulas for these maps, and then give a number of applications. For example, we produce a formula for the Frobenius homomorphisms of Thom spectra such as $\MU$ as well as certain lifts of Frobenius. We prove a rigidity property of $\MU$ as a \emph{cyclotomic} object. We construct a general obstruction theory for $\E_n$ complex orientations and establish various non-existence results for $p$-typical $\E_n$ orientations for low values of $p$ and $n$. We end with some miscellaneous further applications. |
| title | Tate-valued Characteristic Classes II: Applications |
| topic | Algebraic Topology 55R40 |
| url | https://arxiv.org/abs/2510.01488 |