K-theory of Boutet de Monvel's algebra

• Autorzy: Severino T. Melo , Ryszard Nest , Elmar Schrohe
• Języki publikacji: EN

Abstrakty

EN

We consider the norm closure 𝔄 of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a compact manifold X with boundary ∂X. Assuming that all connected components of X have nonempty boundary, we show that K₁(𝔄) ≃ K₁(C(X)) ⊕ ker χ, where χ: K₀(C₀(T*Ẋ)) → ℤ is the topological index, T*Ẋ denoting the cotangent bundle of the interior. Also K₀(𝔄) is topologically determined. In case ∂X has torsion free K-theory, we get K₀(𝔄) ≃ K₀(C(X)) ⊕ K₁(C₀(T*Ẋ)).

Kategorie tematyczne

• 19K56: Index theory
• 58J32: Boundary value problems on manifolds
• 35S15: Boundary value problems for pseudodifferential operators
• 58J40: Pseudodifferential and Fourier integral operators on manifolds
• 46L80: K -theory and operator algebras (including cyclic theory)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2003
• Tom: 61
• Numer: 1
• Strony: 149-156

Daty

wydano

2003

Twórcy

autor

Severino T. Melo

• Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, 05311-970 São Paulo, Brazil

autor

Ryszard Nest

• Department of Mathematics, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark

autor

Elmar Schrohe

• Institut für Mathematik, Universität Potsdam, Postfach 601553, 14415 Potsdam, Germany

Identyfikatory

DOI

10.4064/bc61-0-10