Extending Adams' theorem from singly generated to periodic cohomology
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910758796787712 |
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| author | Harper, John R. Kennard, Lee |
| author_facet | Harper, John R. Kennard, Lee |
| contents | In 1960, J.F. Adams introduced secondary cohomology operations that are defined on cohomology elements on which sufficiently many Steenrod algebra elements vanish. This led to his theorem on singly generated cohomology rings, which in turn led to his celebrated resolution of the Hopf invariant one problem. Here we advertise a conjecture that would extend Adams' result and prove it in a special case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16340 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extending Adams' theorem from singly generated to periodic cohomology Harper, John R. Kennard, Lee Algebraic Topology Differential Geometry K-Theory and Homology 55S10 (Primary) 20F50, 53C20, 55R45, 55S20 In 1960, J.F. Adams introduced secondary cohomology operations that are defined on cohomology elements on which sufficiently many Steenrod algebra elements vanish. This led to his theorem on singly generated cohomology rings, which in turn led to his celebrated resolution of the Hopf invariant one problem. Here we advertise a conjecture that would extend Adams' result and prove it in a special case. |
| title | Extending Adams' theorem from singly generated to periodic cohomology |
| topic | Algebraic Topology Differential Geometry K-Theory and Homology 55S10 (Primary) 20F50, 53C20, 55R45, 55S20 |
| url | https://arxiv.org/abs/2412.16340 |