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K-theory of Boutet de Monvel's algebra

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Melo S., Nest R., Schrohe E.

Banach Center Publications

2003

tom 61

nr 1

149-156

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)).

Ograniczanie wyników

1 Banach Center Publications

1 Melo S.

1 Nest R.

1 Schrohe E.

1 2003

Wyniki wyszukiwania

K-theory of Boutet de Monvel's algebra