We show that elliptic complexes of (pseudo) differential operators on smooth compact manifolds with boundary can always be complemented to a Fredholm problem by boundary conditions involving global pseudodifferential projections on the boundary (similarly as the spectral boundary conditions of Atiyah, Patodi, and Singer for a single operator). We prove that boundary conditions without projections can be chosen if, and only if, the topological Atiyah–Bott obstruction vanishes. These results make use of a Fredholm theory for complexes of operators in algebras of generalized pseudodifferential operators of Toeplitz type which we also develop in the present paper

Elliptic Complexes on Manifolds with Boundary

J. Seiler
2019-01-01

Abstract

We show that elliptic complexes of (pseudo) differential operators on smooth compact manifolds with boundary can always be complemented to a Fredholm problem by boundary conditions involving global pseudodifferential projections on the boundary (similarly as the spectral boundary conditions of Atiyah, Patodi, and Singer for a single operator). We prove that boundary conditions without projections can be chosen if, and only if, the topological Atiyah–Bott obstruction vanishes. These results make use of a Fredholm theory for complexes of operators in algebras of generalized pseudodifferential operators of Toeplitz type which we also develop in the present paper
2019
29
1
656
706
https://link.springer.com/article/10.1007/s12220-018-0014-6
https://arxiv.org/abs/1510.02455
Elliptic complexes, manifolds with boundary
B.-W. Schulze, J. Seiler
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1669119
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