The Journal of Geometric Analysis

, Volume 29, Issue 1, pp 656–706 | Cite as

Elliptic Complexes on Manifolds with Boundary

  • B.-W. Schulze
  • J. SeilerEmail author


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 Manifolds with boundary Atiyah–Bott obstruction Toeplitz-type pseudodifferential operators 

Mathematics Subject Classification

Primary 58J10 47L15 Secondary 35S15 58J40 


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Authors and Affiliations

  1. 1.Universität Potsdam, Institut für MathematikPotsdamGermany
  2. 2.Dipartimento di MatematicaUniversità di TorinoTurinItaly

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