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

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

Algebraic Topology 2025-12-09 v2

Authors: Zhipeng Duan , Michael A. Hill , Guchuan Li , Yutao Liu , XiaoLin Danny Shi , Guozhen Wang , Zhouli Xu

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.

Keywords

higher real K-theories periodicity Morava stabilizer group Lubin-Tate theory RO(G)-graded homotopy groups

Cite

@article{arxiv.2512.01161,
  title  = {Periodicity and finite complexity in higher real $K$-theories},
  author = {Zhipeng Duan and Michael A. Hill and Guchuan Li and Yutao Liu and XiaoLin Danny Shi and Guozhen Wang and Zhouli Xu},
  journal= {arXiv preprint arXiv:2512.01161},
  year   = {2025}
}

Comments

Corrected typos. 40 pages, 9 figures. Comments welcome!

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

Abstract

Keywords

Cite

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