Boote, Yumi
(2016)
*On the symmetric square of quaternionic projective space.*
Doctoral thesis, Manchester Institute for Mathematical Sciences, The University of Manchester.

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## Abstract

The main purpose of this thesis is to calculate the integral cohomology ring of the symmetric square of quaternionic projective space, which has been an open problem since computations with symmetric squares were first proposed in the 1930's. The geometry of this particular case forms an essential part of the thesis, and unexpected results concerning two universal Pin(4) bundles are also included. The cohomological computations involve a commutative ladder of long exact sequences, which arise by decomposing the symmetric square and the corresponding Borel space in compatible ways. The geometry and the cohomology of the configuration space of unordered pairs of distinct points in quaternionic projective space, and of the Thom space MPin(4), also feature, and seem to be of independent interest.

Item Type: | Thesis (Doctoral) |
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Uncontrolled Keywords: | Borel space, configuration space, integral cohomology ring, Pin group, quaternionic projective space, symmetric square. |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 55 Algebraic topology |

Depositing User: | Mrs Yumi Boote |

Date Deposited: | 29 Mar 2016 |

Last Modified: | 20 Oct 2017 14:13 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/2456 |

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