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arXiv · 1510.02455

Elliptic complexes on manifolds with boundary

B. -W. Schulze·J. Seiler
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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.

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B. -W. Schulze, J. Seiler. 2020-04-27. Elliptic complexes on manifolds with boundary. https://doi.org/10.1007/s12220-018-0014-6

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