Work

The $RO(C_2)$-graded Hurewicz image of Atiyah's Real K-theory

Year: 2026

Type: preprint

Abstract: We determine the $RO(C_2)$-graded $k\mathbb R$-Hurewicz image, where $k \mathbb R$ denotes the connective Atiyah's Real $K$-theory spectrum. As a consequence, we obtain four infinite families in the $RO(C_2)$-graded equivariant stable stems that are $C_2$-equivariant refinements of the classical $μ$-families. Using a $C_2$-equivariant $v_{1,0}$-self map, we explicitly construct an equivariant Adams periodicity operator $P_{C_2}$ that captures these $v_1$-periodicity phenomena in the $C_2$-stable stems.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.19606

Authors: Ma, Sihao, Shi, Xiaolin Danny, Xu, Zhouli, Yang, Albert Jinghui, Zhang, Shangjie

Institutions: University of California, Los Angeles, University of Washington, University of Pennsylvania

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7222308866

Cites: 5

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Related to: 10