Refine
Year of publication
Document Type
- Preprint (45)
- Monograph/Edited Volume (39)
- Article (26)
Language
- English (110)
Keywords
- K-theory (7)
- elliptic operators (6)
- relative index (6)
- Atiyah-Patodi-Singer theory (5)
- Fredholm property (5)
- index theory (5)
- boundary value problems (4)
- elliptic operator (4)
- index (4)
- manifold with singularities (4)
Institute
We define a class of boundary value problems on manifolds with fibered boundary. This class is in a certain sense a deformation between the classical boundary value problems and the Atiyah-Patodi-Singer problems in subspaces (it contains both as special cases). The boundary conditions in this theory are taken as elements of the C*-algebra generated by pseudodifferential operators and families of pseudodifferential operators in the fibers. We prove the Fredholm. property for elliptic boundary value problems and compute a topological obstruction (similar to Atiyah-Bott obstruction) to the existence of elliptic boundary conditions for a given elliptic operator. Geometric operators with trivial and nontrivial obstruction are given. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Necessary and sufficient conditions for the representation of the index of elliptic operators on manifolds with edges in the form of the sum of homotopy invariants of symbols on the smooth stratum and on the edge are found. An index formula is obtained for elliptic operators on manifolds with edges under symmetry conditions with respect to the edge covariables