On the K-theory of the loop space of a Lie group
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...
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University of Warwick
1971
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ndltd-bl.uk-oai-ethos.bl.uk-4516162015-10-03T03:19:57ZOn the K-theory of the loop space of a Lie groupClarke, Francis Willoughby1971The 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.510QA MathematicsUniversity of Warwickhttp://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.451616http://wrap.warwick.ac.uk/71428/Electronic Thesis or Dissertation |
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NDLTD |
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NDLTD |
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510 QA Mathematics |
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510 QA Mathematics Clarke, Francis Willoughby On the K-theory of the loop space of a Lie group |
| description |
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. |
| author |
Clarke, Francis Willoughby |
| author_facet |
Clarke, Francis Willoughby |
| author_sort |
Clarke, Francis Willoughby |
| title |
On the K-theory of the loop space of a Lie group |
| title_short |
On the K-theory of the loop space of a Lie group |
| title_full |
On the K-theory of the loop space of a Lie group |
| title_fullStr |
On the K-theory of the loop space of a Lie group |
| title_full_unstemmed |
On the K-theory of the loop space of a Lie group |
| title_sort |
on the k-theory of the loop space of a lie group |
| publisher |
University of Warwick |
| publishDate |
1971 |
| url |
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.451616 |
| work_keys_str_mv |
AT clarkefranciswilloughby onthektheoryoftheloopspaceofaliegroup |
| _version_ |
1716825959094550528 |