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Severino T Melo, Thomas Schick, Elmar Schrohe

A K-theoretic proof of Boutet de Monvel's index theorem for boundary value problems

We study the C*-closure of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a compact connected manifold X with boundary . We find short exact sequences in K-theory which split, so that K_i( ) ≅ K_i(C(X)) ⊕ K_1−i(C₀(T*X°)). Using only simple K-theoretic arguments and the Atiyah-Singer index theorem, we show that the Fredholm index of an elliptic element in 𝒜 is given by where [A] is the class of A in K₁( ) and ind_t is the topological index, a relation first established by Boutet de Monvel by different methods.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2006, 10/2006
Pages: 217 - 233

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