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.
Date of Award  1 Aug 2016 

Original language  English 

Awarding Institution   The University of Manchester


Supervisor  Nigel Ray (Supervisor) & James Montaldi (Supervisor) 

 projective space
 Borel space
 configuration space
 integral cohomology ring
 Pin group
 symmetric square
On the symmetric square of quaternionic projective space
Boote, Y. (Author). 1 Aug 2016
Student thesis: Phd