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arXiv · 2512.01161

Periodicity and finite complexity in higher real $K$-theories

Zhipeng Duan·Michael A. Hill·Guchuan Li·Yutao Liu·XiaoLin Danny Shi·Guozhen Wang·Zhouli Xu
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Abstract

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.

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Zhipeng Duan, Michael A. Hill, Guchuan Li, Yutao Liu, XiaoLin Danny Shi, Guozhen Wang, Zhouli Xu. 2025-12-01. Periodicity and finite complexity in higher real $K$-theories. https://arxiv.org/abs/2512.01161

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