In this thesis we study two of the exceptional projetive planes P2(CO) and P2(HO). These are the homogenous spaces E6/S1 _C4 Spin(10) and E7=S3 _C2 Spin(12). These spaces both have natural actions by the compact Lie groups F4 and S1 x E6 respectively. The method that we will use to study these spaces is via the decompositions associated to these actions. In particular we will describe the homotopy type of P2(CO) in terms of the octonionic projective plane P2(O) and spaces associated to P2(O). We use this to compute the cohomology of P2(CO). Finally, we give a description of certain orbits of the action on P2(HO).
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:682859 |
| Date | January 2015 |
| Creators | Goss, Robert |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/77125/ |
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