2001/10/23 by S. T. Melo, Severino T. Melo, R. Nest +6
Mathematics · #19K56 #35S15 #46L80 #58J32 #58J40 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Analysis of PDEs (math.AP) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #math.AP #math.KT #math.OA #msc:19K56 #msc:35S15 #msc:46L80 #msc:58J32 #msc:58J40
paper · pdf · doi:10.48550/arxiv.math/0110253
Final version, to appear in J. Reine Angew. Math. Improved K-theoretic results
openalex publication_date 2001/10/23 · arxiv created 2002/10/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 manifold X with boundary Y. We first describe the image and the kernel of the continuous extension of the boundary principal symbol to A. If the X is connected and Y is not empty, we then show that the K-groups of A are topologically determined. In case the manifold, its boundary and the tangent space of the interior have torsion-free K-theory, we prove that Ki(A/K) is isomorphic to the direct sum of Ki(C(X)) and K1-i(C0(TX')), for i=0,1, with K denoting the compact ideal and TX' the tangent bundle of the interior of X. Using Boutet de Monvel's index theorem, we also prove this result for i=1 without assuming the torsion-free hypothesis. We also give a composition sequence for A.