具有超过7个向量场的球面：Spin(9)的全部作用
微分几何
2012-05-01 v2 环与代数
摘要
我们给出了球面上最大线性无关向量场数目在R^16上Spin(9)表示中的解释。这揭示了Spin(9)作为SO(16)子群在球面上向量场存在性中的作用，类似于复结构、四元数结构和八元数结构分别在R^2、R^4和R^8中所起的作用。
引用
@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}
}
备注
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