Properties and Examples of $A$-Landweber Exact Spectra
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909092549754880 |
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| author | Wisdom, Noah |
| author_facet | Wisdom, Noah |
| contents | It is classically known that Landweber exact homology theories (complex oriented theories which are completely determined by complex cobordism) admit no nontrivial phantom maps. Herein we propose a definition of $A$-Landweber exact spectra, for $A$ a compact abelian Lie group, and show that an analogous result on phantom maps holds. Also, we show that a conjecture of May on $KU_G$ is false. We do not prove an equivariant Landweber exact functor theorem, and therefore our result on phantom maps only applies to $MU_A$, $KU_A$, their $p$-localizations, and $BP_A$, which are shown to be $A$-Landweber exact by ad-hoc methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_12227 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Properties and Examples of $A$-Landweber Exact Spectra Wisdom, Noah Algebraic Topology 55N22 (Primary) 19L47, 55P92, 55N91 (Secondary) It is classically known that Landweber exact homology theories (complex oriented theories which are completely determined by complex cobordism) admit no nontrivial phantom maps. Herein we propose a definition of $A$-Landweber exact spectra, for $A$ a compact abelian Lie group, and show that an analogous result on phantom maps holds. Also, we show that a conjecture of May on $KU_G$ is false. We do not prove an equivariant Landweber exact functor theorem, and therefore our result on phantom maps only applies to $MU_A$, $KU_A$, their $p$-localizations, and $BP_A$, which are shown to be $A$-Landweber exact by ad-hoc methods. |
| title | Properties and Examples of $A$-Landweber Exact Spectra |
| topic | Algebraic Topology 55N22 (Primary) 19L47, 55P92, 55N91 (Secondary) |
| url | https://arxiv.org/abs/2401.12227 |