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On the K-theory of the loop space of a Lie group

Published online by Cambridge University Press:  24 October 2008

Francis Clarke
Francis Clarke
Affiliation:
Department of Pure Mathematics, University College of Swansea, Wales
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Let G be a simply connected, semi-simple, compact Lie group, let K* denote Z/2-graded, representable K-theory, and K* the corresponding homology theory. The K-theory of G and of its classifying space BG are well known, (8),(1). In contrast with ordinary cohomology, K*(G) and K*(BG) are torsion-free and have simple multiplicative structures. If ΩG denotes the space of loops on G, it seems natural to conjecture that K*(ΩG) should have, in some sense, a more simple structure than H*(ΩG).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 1 , July 1974 , pp. 1 - 20
Copyright
Copyright © Cambridge Philosophical Society 1974

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