A Continuous Field of C*-algebras and the Tangent Groupoid for Manifolds with Boundary

2005/07/15 by Johannes Aastrup, Aastrup, Johannes, Ryszard Nest +3
Mathematics · #35S15 #46L80 #58H05 #58J32 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:35S15 #msc:46L80 #msc:58H05 #msc:58J32

paper · pdf · doi:10.48550/arxiv.math/0507317

arxiv created 2005/07/15 · arxiv updated 2009/12/01

Abstract

For a smooth manifold with boundary we construct a semigroupoid and a continuous field of C*-algebras which extend Connes' construction of the tangent groupoid. We show the asymptotic multiplicativity of ℏ-scaled truncated pseudodifferential operators with smoothing symbols and compute the K-theory of the associated symbol algebra.

Related

• Index Theory for Boundary Value Problems via Continuous Fields of C*-algebras
• Pseudodifferential calculus on manifolds with corners and groupoids
• Differential operators on C*-algebras and applications to smooth functional calculus and Schwartz functions on the tangent groupoid
• Pseudodifferential operators on differential groupoids
• C*-algebras associated with branched coverings