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On the K-theory of the loop space of a Lie group
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Clarke, Francis Willoughby (1971) On the K-theory of the loop space of a Lie group. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b1733212~S1
Abstract
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.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | K-theory, Lie groups, Algebraic topology | ||||
Official Date: | August 1971 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Extent: | 139 leaves | ||||
Language: | eng |
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