In this article, we study the cohomology of Lie algebras of vector fields of holomorphic type V ect1,0(M) on a complex manifold M . The main result is the introduction of a kind of order filtration on the continuous cochains on V ect1,0(M) and the calculation of the second term of the resulting spectral sequence. The filtration is very much in the spirit of the classical order filtration of Gel...

Part 4. K-theory and geometry II 139 20. K∗(CP) and the K-theoretic analog of the degree 139 21. Interlude on the calculus of finite differences 147 22. The Euler class 153 23. Chern classes 165 24. Comparing K-theory and singular cohomology 169 25. The Grothendieck-Riemann-Roch Theorem 176 26. The algebro-geometric GRR theorem 187 27. Formal group laws and complex-oriented cohomology theories 191