A+ CATEGORY SCIENTIFIC UNIT

K-theory of Boutet de Monvel's algebra

Volume 61 / 2003

Severino T. Melo, Ryszard Nest, Elmar Schrohe Banach Center Publications 61 (2003), 149-156 MSC: Primary 58J40, 46L80; Secondary 58J32, 35S15, 19K56. DOI: 10.4064/bc61-0-10

Abstract

We consider the norm closure ${\mathfrak A}$ of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a compact manifold $X$ with boundary $\partial X$. Assuming that all connected components of $X$ have nonempty boundary, we show that $K_1({\mathfrak A})\simeq K_1(C(X))\oplus\ker\chi$, where $\chi:K_0(C_{0}(T^*\dot X))\to{\mathbb Z}$ is the topological index, $T^*\dot X$ denoting the cotangent bundle of the interior. Also $K_0({\mathfrak A})$ is topologically determined. In case $\partial X$ has torsion free K-theory, we get $K_0({\mathfrak A})\simeq K_0(C(X))\oplus K_1(C_{0}(T^*\dot X))$.

Authors

  • Severino T. MeloInstituto de Matemática e Estatística
    Universidade de São Paulo
    Caixa Postal 66281
    05311-970 São Paulo, Brazil
    e-mail
  • Ryszard NestDepartment of Mathematics
    University of Copenhagen
    Universitetsparken 5
    2100 Copenhagen, Denmark
    e-mail
  • Elmar SchroheInstitut für Mathematik
    Universität Potsdam
    Postfach 601553
    14415 Potsdam, Germany
    e-mail

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