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- W2032459103 abstract "We prove an index theorem for boundary value problems in Boutet de Monvel's calculus on a compact manifold X with boundary. The basic tool is the tangent semigroupoid $cT^-X$ generalizing the tangent groupoid defined by Connes in the boundaryless case, and an associated continuous field C*_r(cT^-X) of C*-algebras over [0,1]. Its fiber in h=0, C*_r(T^-X), can be identified with the symbol algebra for Boutet de Monvel's calculus; for hnot=0 the fibers are isomorphic to the algebra K of compact operators. We therefore obtain a natural map K_0(C*_r(T^-X))=K_0(C_0(T*X)) -> K_0(K)=Z. Using deformation theory we show that this is the analytic index map. On the other hand, using ideas from noncommutative geometry, we construct the topological index map and prove that it coincides with the analytic index map." @default.
- W2032459103 created "2016-06-24" @default.
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- W2032459103 date "2008-12-02" @default.
- W2032459103 modified "2023-09-28" @default.
- W2032459103 title "Index Theory for Boundary Value Problems via Continuous Fields of C*-algebras" @default.
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