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Boundary value problems on manifolds with fibered boundary

✍ Scribed by Anton Savin; Boris Sternin

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
243 KB
Volume
278
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

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. (Β© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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