K-theory of Boutet de Monvel's algebra

Severino 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 -