Periodicity and finite complexity in higher real $K$-theories
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917128711438336 |
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| author | Duan, Zhipeng Hill, Michael A. Li, Guchuan Liu, Yutao Shi, XiaoLin Danny Wang, Guozhen Xu, Zhouli |
| author_facet | Duan, Zhipeng Hill, Michael A. Li, Guchuan Liu, Yutao Shi, XiaoLin Danny Wang, Guozhen Xu, Zhouli |
| contents | In this paper, we establish periodicity results for higher real $K$-theories at all heights and for all finite subgroups of the Morava stabilizer group at the prime 2. We further analyze the $RO(G)$-periodicity lattice of the height-$h$ Lubin--Tate theory, proving new $RO(G)$-graded periodicities and explicit finiteness results for the $RO(G)$-graded homotopy groups of $E_h$. Together, these results provide a foundation for both the structural and computational study of higher real $K$-theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01161 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Periodicity and finite complexity in higher real $K$-theories Duan, Zhipeng Hill, Michael A. Li, Guchuan Liu, Yutao Shi, XiaoLin Danny Wang, Guozhen Xu, Zhouli Algebraic Topology In this paper, we establish periodicity results for higher real $K$-theories at all heights and for all finite subgroups of the Morava stabilizer group at the prime 2. We further analyze the $RO(G)$-periodicity lattice of the height-$h$ Lubin--Tate theory, proving new $RO(G)$-graded periodicities and explicit finiteness results for the $RO(G)$-graded homotopy groups of $E_h$. Together, these results provide a foundation for both the structural and computational study of higher real $K$-theories. |
| title | Periodicity and finite complexity in higher real $K$-theories |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2512.01161 |