English

Immersions of $C_2$-projective spaces via $K\mathbb{R}$-theory

Algebraic Topology 2026-04-29 v1 Geometric Topology K-Theory and Homology

Abstract

We compute the Atiyah Real KK-theory of C2C_2-equivariant projective spaces and construct immersions of such spaces into multiples of the regular representation. These computations are made tractable by the recent geometric filtration of equivariant projective spaces due to Bhattacharya-Waugh-Zeng-Zou, together with a variant of the localized slice spectral sequence introduced by Meier-Shi-Zeng. As an immediate corollary of these computations, we obtain an equivariant analogue of James periodicity.

Keywords

Cite

@article{arxiv.2604.25260,
  title  = {Immersions of $C_2$-projective spaces via $K\mathbb{R}$-theory},
  author = {Manyi Guo and Jackson Morris and Alex Waugh and Albert Jinghui Yang},
  journal= {arXiv preprint arXiv:2604.25260},
  year   = {2026}
}

Comments

32 pages, 15 figures