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arXiv · 1107.0462

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

Maurizio Parton·Paolo Piccinni
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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, R^4 and R^8, respectively.

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Maurizio Parton, Paolo Piccinni. 2011-07-03. Spheres with more than 7 vector fields: all the fault of Spin(9). https://arxiv.org/abs/1107.0462

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