# K-theory of Boutet de Monvel's algebra

Severino T. Melo; Ryszard Nest; Elmar Schrohe

Banach Center Publications (2003)

- Volume: 61, Issue: 1, page 149-156
- ISSN: 0137-6934

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topSeverino T. Melo, Ryszard Nest, and Elmar Schrohe. "K-theory of Boutet de Monvel's algebra." Banach Center Publications 61.1 (2003): 149-156. <http://eudml.org/doc/282178>.

@article{SeverinoT2003,

abstract = {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)).},

author = {Severino T. Melo, Ryszard Nest, Elmar Schrohe},

journal = {Banach Center Publications},

keywords = {Boutet de Monvel algebra; boundary value problem; K-theory},

language = {eng},

number = {1},

pages = {149-156},

title = {K-theory of Boutet de Monvel's algebra},

url = {http://eudml.org/doc/282178},

volume = {61},

year = {2003},

}

TY - JOUR

AU - Severino T. Melo

AU - Ryszard Nest

AU - Elmar Schrohe

TI - K-theory of Boutet de Monvel's algebra

JO - Banach Center Publications

PY - 2003

VL - 61

IS - 1

SP - 149

EP - 156

AB - 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)).

LA - eng

KW - Boutet de Monvel algebra; boundary value problem; K-theory

UR - http://eudml.org/doc/282178

ER -

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