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Spheres with more than 7 vector fields: all the fault of Spin(9) (1107.0462v2)

Published 3 Jul 2011 in math.DG and math.RA

Abstract: We give an interpretation of the maximal number of linearly independent vector fields on spheres in terms of the Spin(9) representation on R^16. This casts an insight on the role of Spin(9) as a subgroup of SO(16) on the existence of vector fields on spheres, parallel to the one played by complex, quaternionic and octonionic structures on R^2, R⁴ and R^8, respectively.