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THE C1-Invariance of the Godbillon-Vey Map in Analytical K-Theory

Published online by Cambridge University Press:  20 November 2018

Toshikazu Natsume
Toshikazu Natsume*
Affiliation:
University of Copenhagen, Copenhagen, Denmark
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An action α of a discrete group Γ on the circle S1 as orientation preserving C∞-diffeomorphisms gives rise to a foliation on the homotopy quotient S1Γ, and its Godbillon-Vey invariant is, by definition, a cohomology class of S1Γ([1]). This cohomology class naturally defines an additive map from the geometric K-group K0(S1, Γ) into C, through the Chern character from K0(S1, Γ) to H*(S1, Γ Q).

Using cyclic cohomology, Connes constructed in [2] an additive map, GV(α), which we shall call the Godbillon-Vey map, from the K0-group of the reduced crossed product C*-algebra C(S1) ⋊ αΓ into C. He showed that GV(α) agrees with the geometric Godbillon-Vey invariant through the index map μ from K0(S1, Γ) to K0(C(S1) ⋊ αΓ).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 5 , 01 October 1987 , pp. 1210 - 1222
Copyright
Copyright © Canadian Mathematical Society 1987

References

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