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PreprintCC BY-NC-SA 4.0arXiv

The RO(C2)-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(C2)-graded kℝ-Hurewicz image, where k ℝ denotes the connective Atiyah's Real K-theory spectrum. As a consequence, we obtain four infinite families in the RO(C2)-graded equivariant stable stems that are C2-equivariant refinements of the classical μ-families. Using a C2-equivariant v1,0-self map, we explicitly construct an equivariant Adams periodicity operator PC2 that captures these v1-periodicity phenomena in the C2-stable stems.

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Cite

BibTeXRIS
BibTeX
@misc{ma2026roc2graded,
  title = {{The $RO(C_2)$-graded Hurewicz image of Atiyah's Real K-theory}},
  author = {Sihao Ma and Xiaolin Danny Shi and Zhouli Xu and Albert Jinghui Yang and Shangjie Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19606},
  eprint = {2610.19606},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19606},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - The RO(C_2)-graded Hurewicz image of Atiyah's Real K-theory
AU  - Sihao Ma
AU  - Xiaolin Danny Shi
AU  - Zhouli Xu
AU  - Albert Jinghui Yang
AU  - Shangjie Zhang
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.19606
UR  - https://arxiv.org/abs/2610.19606
AB  - We determine the RO(C_2)-graded kℝ-Hurewicz image, where k 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.
ER  -