A K-Theoretic Proof of Boutet de Monvel's Index Theorem for Boundary Value Problems
| dc.creator | Melo, Severino T. | |
| dc.creator | Schick, Thomas | |
| dc.creator | Schrohe, Elmar | |
| dc.date | 2004-03-03 | |
| dc.date | 2005-10-11 | |
| dc.date.accessioned | 2026-07-07T07:49:05Z | |
| dc.date.available | 2026-07-07T07:49:05Z | |
| dc.description | We study the C*-closure A of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a compact connected manifold X with non-empty boundary. We find short exact sequences in K-theory 0->K_i(C(X))->K_i(A/K)->K_{1-i}(C_0(T*X'))->0, i= 0,1, which split, where K denotes the compact ideal and T*X' the cotangent bundle of the interior of X. Using only simple K-theoretic arguments and the Atiyah-Singer Index Theorem, we show that the Fredholm index of an elliptic element in A is given as the composition of the topological index with mapping K_1(A/K)->K_0(C_0(T*X')) defined above. This relation was first established by Boutet de Monvel by different methods. | |
| dc.description | Title slightly changed. Accepted for publication in Journal fuer die reine und angewandte Mathematik | |
| dc.identifier | https://arxiv.org/abs/math/0403059 | |
| dc.identifier | http://arxiv.org/abs/math/0403059 | |
| dc.identifier | J. reine angew. Math. 599 (2006), 217-233 | |
| dc.identifier | doi:10.1515/CRELLE.2006.083 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124722 | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 58J32; 19K56; 46L80 | |
| dc.title | A K-Theoretic Proof of Boutet de Monvel's Index Theorem for Boundary Value Problems | |
| dc.type | text |