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arXiv · 2610.19606

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

Sihao Ma·Xiaolin Danny Shi·Zhouli Xu·Albert Jinghui Yang·Shangjie Zhang
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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.

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Sihao Ma, Xiaolin Danny Shi, Zhouli Xu, Albert Jinghui Yang, Shangjie Zhang. 2026-10-14. The $RO(C_2)$-graded Hurewicz image of Atiyah's Real K-theory. https://arxiv.org/abs/2610.19606

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