Duals of higher real $K$-theories at $p=2$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910649305530368 |
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| author | Del Angel, Juan C. Moreno |
| author_facet | Del Angel, Juan C. Moreno |
| contents | We study $\mathrm{K}(h)$-local Spanier-Whitehead duality for $C_{2^n}$-equivariant Lubin-Tate spectra, $E_h$, at the prime $2$ and heights $h$ divisible by $2^{n-1}$. We determine a $C_{2^n}$-equivariant equivalence $DE_h\simeqΣ^{-V_h} E_h$, for an explicit $C_{2^n}$-representation, $V_h$. We then study the $\mathrm{RO}(C_{2^n})$-periodicities of $E_h$ at some low heights. With these ingredients, we determine the self-duality of some higher real $K$-theories up to a specified suspension shift, at some low-heights. In particular, we show that $DE_4^{hC_8}\simeq Σ^{112}E_4^{hC_8}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10726 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Duals of higher real $K$-theories at $p=2$ Del Angel, Juan C. Moreno Algebraic Topology We study $\mathrm{K}(h)$-local Spanier-Whitehead duality for $C_{2^n}$-equivariant Lubin-Tate spectra, $E_h$, at the prime $2$ and heights $h$ divisible by $2^{n-1}$. We determine a $C_{2^n}$-equivariant equivalence $DE_h\simeqΣ^{-V_h} E_h$, for an explicit $C_{2^n}$-representation, $V_h$. We then study the $\mathrm{RO}(C_{2^n})$-periodicities of $E_h$ at some low heights. With these ingredients, we determine the self-duality of some higher real $K$-theories up to a specified suspension shift, at some low-heights. In particular, we show that $DE_4^{hC_8}\simeq Σ^{112}E_4^{hC_8}$. |
| title | Duals of higher real $K$-theories at $p=2$ |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2410.10726 |