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arXiv · 2306.17709

The Structure of the Spin^h Bordism Spectrum

Keith Mills
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Abstract

Spin$^h$ manifolds are the quaternionic analogue to Spin$^c$ manifolds. We compute the spin$^h$ bordism groups at the prime 2 by proving a structure theorem for the cohomology of the spin$^h$ bordism spectrum $\mathrm{MSpin}^h$ as a module over the mod 2 Steenrod algebra. This provides a 2-local splitting of $\mathrm{MSpin}^h$ as a wedge sum of familiar spectra. We also compute the decomposition of $H^*(\mathrm{MSpin}^h;\mathbb{Z}/2\mathbb{Z})$ explicitly in degrees up through 30 via a counting process.

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Keith Mills. 2023-06-30. The Structure of the Spin^h Bordism Spectrum. https://arxiv.org/abs/2306.17709

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