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Title: On the K-theory of the loop space of a Lie group
Author: Clarke, Francis Willoughby
ISNI:       0000 0001 3557 6972
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1971
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The thesis studies the K-theory of the loop space of compact Lie groups. There are three independent chapters. The first chapter is devoted to proving the non-convergence of a K-theory Eilenberg-Maclane spectral sequence for the path space fibration on a Lie group with torsion in its cohomology. The second chapter generalises a method of Bott. We obtain an algebraic expression for K*(ΩG) in terms of the" representation theory of the group G. Explicit results are obtained for the unitary groups and the first symplectic group. The third chapter develops and extends a method due to T. Petrie to find the Hopf algebra structure of the complex bordism of .ΩG. The Conner-Floyd isomorphism is used to obtain explicit results for K*(ΩG) for a larger class of groups than in chapter two.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics