More on the K-theory of the Boutet de Monvel algebra

Autors: Melo, S., Schick, T., and Schrohe, E.
Titel: A K-theoretic proof of Boutet de Monvel's index theorem (dvi) (pdf)
preprint, Göttingen

Let A denote the C*-closure of the algebra of all polyhomogeneous operators of order and class zero in Boutet de Monvel's calculus on a connected manifold X with nonempty boundary. We derive a short exact sequence 0->K_i(C(X))->K_i(A/K)->K_{1-i}(TX')->0, which splits in a not necessarily natural way. Here K is the compact ideal and TX' is the cotangent bundle of the interior of X. We also give a K-theoretic proof of the fact that the composition of the topological index with the mapping from K_1(A/K) to K_0(TX') in the above sequence gives the Fredholm-index homomorphism. That the Fredholm index for A factors through K(TX') was first proven by Boutet de Monvel.

Thomas Schick