The Real-oriented cohomology of infinite stunted projective spaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909430913695744 |
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| author | Balderrama, William |
| author_facet | Balderrama, William |
| contents | Let $E\mathbb{R}$ be an even-periodic Real Landweber exact $C_2$-spectrum, and $ER$ its spectrum of fixed points. We compute the $ER$-cohomology of the infinite stunted projective spectra $P_j$. These cohomology groups combine to form the $RO(C_2)$-graded coefficient ring of the $C_2$-spectrum $b(ER) = F(EC_{2+},i_\ast ER)$, which we show is related to $E\mathbb{R}$ by a cofiber sequence $Σ^σb(ER)\rightarrow b(ER)\rightarrow E\mathbb{R}$. We illustrate our description of $π_\star b(ER)$ with the computation of some $ER$-based Mahowald invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_06934 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Real-oriented cohomology of infinite stunted projective spaces Balderrama, William Algebraic Topology Let $E\mathbb{R}$ be an even-periodic Real Landweber exact $C_2$-spectrum, and $ER$ its spectrum of fixed points. We compute the $ER$-cohomology of the infinite stunted projective spectra $P_j$. These cohomology groups combine to form the $RO(C_2)$-graded coefficient ring of the $C_2$-spectrum $b(ER) = F(EC_{2+},i_\ast ER)$, which we show is related to $E\mathbb{R}$ by a cofiber sequence $Σ^σb(ER)\rightarrow b(ER)\rightarrow E\mathbb{R}$. We illustrate our description of $π_\star b(ER)$ with the computation of some $ER$-based Mahowald invariants. |
| title | The Real-oriented cohomology of infinite stunted projective spaces |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2207.06934 |