Spheres with more than 7 vector fields: all the fault of Spin(9)
Differential Geometry
2012-05-01 v2 Rings and Algebras
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.
Keywords
Cite
@article{arxiv.1107.0462,
title = {Spheres with more than 7 vector fields: all the fault of Spin(9)},
author = {Maurizio Parton and Paolo Piccinni},
journal= {arXiv preprint arXiv:1107.0462},
year = {2012}
}
Comments
14 pages. Revised version. The proof of the main theorem, now without induction, is in the completely new Section 6. Notations have been simplified in all the paper