Use this URL to cite or link to this record in EThOS:  https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.749786 
Title:  Homotopy theory of gauge groups over certain 7manifolds  
Author:  Membrillo Solis, Ingrid Amaranta 
ISNI:
0000 0004 7234 2114


Awarding Body:  University of Southampton  
Current Institution:  University of Southampton  
Date of Award:  2017  
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Abstract:  
The gauge groups of principal Gbundles over low dimensional spaces have been extensively studied in homotopy theory due to their connections to other areas in mathematics, such as the YangMills gauge theory in mathematical physics. In 2011 Donaldson and Segal established the mathematical setup to construct new gauge theories over high dimensional spaces. In this thesis we study the homotopy theory of gauge groups over 7manifolds that arise as total spaces of S 3 bundles over S 4 and their connected sums. We classify principal Gbundles over manifolds M up to isomorphism in the following cases: (1) M is an S 3 bundle over S 4 with torsionfree homology; (2) M is an S 3 bundle over S 4 with nontorsionfree homology and π6(G) = 0; (3) M is a connected sum of S 3 bundles over S 4 with torsionfree homology and π6(G) = 0. We obtain integral homotopy decomposition of the gauge groups in the cases for which the manifold is either a product of spheres, or a twisted product of spheres, or a connected sum of those. We obtain plocal homotopy decompositions of the loop spaces of the gauge groups in the cases for which the manifold has torsion in homology. Gauge groups of principal Gbundles over manifolds homotopy equivalent to S 7 are classified up to a plocal homotopy equivalence.


Supervisor:  Theriault, Stephen  Sponsor:  Not available  
Qualification Name:  Thesis (Ph.D.)  Qualification Level:  Doctoral  
EThOS ID:  uk.bl.ethos.749786  DOI:  Not available  
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