Index Theory for Boundary Value Problems via Continuous Fields of C*-algebras

Details Index Theory for Boundary Value Problems via Continuous Fields of C*-algebras Index Theory for Boundary Value Problems via Continuous Fields of C*-algebras

2008-12-02

arxiv.org/abs/0812.0554v1

Mathematics

Functional Analysis

Scientific paper

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 h\not=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.

Affiliated with

Also associated with

No associations

Rating

Index Theory for Boundary Value Problems via Continuous Fields of C*-algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Index Theory for Boundary Value Problems via Continuous Fields of C*-algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Index Theory for Boundary Value Problems via Continuous Fields of C*-algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-719001