The Structure of the Spin^h Bordism Spectrum

2023/06/30 by Mills, Keith
#55N22 (Primary) 55T15 #55S10 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.17709

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 MSpin^h as a module over the mod 2 Steenrod algebra. This provides a 2-local splitting of MSpin^h as a wedge sum of familiar spectra. We also compute the decomposition of H^*(MSpin^h;ℤ/2ℤ) explicitly in degrees up through 30 via a counting process.

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