Some Group Actions on Homotopy Spheres of Dimension Seven and Fifteen

@article{Davis1982SomeGA,
  title={Some Group Actions on Homotopy Spheres of Dimension Seven and Fifteen},
  author={Michael W. Davis},
  journal={American Journal of Mathematics},
  year={1982},
  volume={104},
  pages={59}
}
  • Michael W. Davis
  • Published 1 February 1982
  • Mathematics
  • American Journal of Mathematics
0. Introduction. This paper is based on the simple observation that every 4-plane bundle over S4 admits a natural action of 50(3) by bundle maps and that every 8-plane bundle over 58 admits a natural action of the compact Lie group G2 by bundle maps. (These actions are easy to see once one remembers that SO (3) is the group of automorphisms of the quaternions and that G2 is the group of automorphisms of the Cayley numbers.) The study of these actions is closely connected to several well-known… 
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