TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Seiler, Jörg
T1  - Elliptic complexes on manifolds with boundary
JF  - The journal of geometric analysis
N2  - 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.
KW  - Elliptic complexes
KW  - Manifolds with boundary
KW  - Atiyah-Bott obstruction
KW  - Toeplitz-type pseudodifferential operators
Y1  - 2018
U6  - https://doi.org/10.1007/s12220-018-0014-6
SN  - 1050-6926
SN  - 1559-002X
VL  - 29
IS  - 1
SP  - 656
EP  - 706
PB  - Springer
CY  - New York
ER  -