Boundary Value Problems on Manifolds with Fibered Boundary

Details Boundary Value Problems on Manifolds with Fibered Boundary Boundary Value Problems on Manifolds with Fibered Boundary

2002-07-20

arxiv.org/abs/math/0207179v1

Math. Nachr. 278 (2005), no. 11, 1297-1317

Mathematics

Operator Algebras

30 pages

Scientific paper

10.1002/mana.200410308

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. 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. This class also contains nonlocal boundary value problems of math.KT/0108107. We compute a topological obstruction (similar to the Atiyah-Bott obstruction) to the existence of elliptic boundary conditions for a given operator. Geometric operators with a nontrivial obstruction are given.

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