THE STRUCTURE OF THE SPIN h BORDISM SPECTRUM

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 & lowast; (MSpin h ; Z /2 Z ) explicitly in degrees up through 30 via a counting process.