THE C1-Invariance of the Godbillon-Vey Map in Analytical K-Theory
Keyword(s):
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).
2006 ◽
Vol 207
(2)
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pp. 455-483
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1990 ◽
Vol 20
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pp. 637-650
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2003 ◽
Vol 236
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pp. 161-186
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Keyword(s):
2012 ◽
Vol 140
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pp. 745-747