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The Structure of the Spin^h Bordism Spectrum
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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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Cited by 1 Pith paper
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Global Structure in the Presence of a Topological Defect
Characteristic structures on manifolds with codimension-2 defects are translated into twisted spin bordism, low-degree groups are computed, and a Pontryagin-Thom obstruction to breaking Z/2 higher-form symmetries is i...
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