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The K-theory of the C*-algebra of foliations by slope components

Published online by Cambridge University Press:  28 May 2008

Catherine Oikonomides
Catherine Oikonomides
Affiliation:
Department of Mathematics, Keio University, 3-14-1 Hiyoshi Kohoku-ku, Yokohama, Japan, oikonomi@math.keio.ac.jp.
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Abstract

We compute the K-theory of the C*-algebra for a large class of foliations of the 3-torus, which contains in particular all smooth foliated circle bundles over the 2-torus. This generalizes a well-known result of Torpe. We show that the rank of the K-theory groups reflect part of the geometrical aspect of the foliation. To illustrate these results, we compute some concrete examples, including a case where both K-theory groups have infinite rank.

Keywords

FoliationsC*-algebrasK-theory
Type
Research Article
Information
Journal of K-Theory , Volume 3 , Issue 2 , April 2009 , pp. 221 - 260
Copyright
Copyright © ISOPP 2009

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