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arXiv · 2511.10624

The homotopy fixed points of Real spin bordism

Hassan H. Abdallah·Yigal Kamel
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Abstract

We show that the 2-local splitting of spin$^c$ bordism by Anderson--Brown--Peterson and Stong refines to a $C_2$-equivariant map in the category of spectra with $C_2$-action from Real spin bordism to a sum of (higher) connective covers of $\mathrm{ku}_{\mathbb{R}}$ and suspensions of mod 2 Eilenberg--Mac Lane spectra. We use this to deduce a corresponding 2-local splitting of the homotopy fixed points of Real spin bordism. We also discuss prospects that arise in the genuine setting.

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Hassan H. Abdallah, Yigal Kamel. 2025-11-13. The homotopy fixed points of Real spin bordism. https://arxiv.org/abs/2511.10624

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