@article{SchulzeSeiler2019,
  author    = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg},
  title     = {Elliptic complexes on manifolds with boundary},
  series = {The journal of geometric analysis},
  volume    = {29},
  journal   = {The journal of geometric analysis},
  number    = {1},
  publisher = {Springer},
  address   = {New York},
  issn      = {1050-6926},
  doi       = {10.1007/s12220-018-0014-6},
  pages     = {656 -- 706},
  year      = {2019},
  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.},
  language  = {en}
}
@article{Wallenta2014,
  author    = {Wallenta, Daniel},
  title     = {A Lefschetz fixed point formula for elliptic quasicomplexes},
  series = {Integral equations and operator theor},
  volume    = {78},
  journal   = {Integral equations and operator theor},
  number    = {4},
  publisher = {Springer},
  address   = {Basel},
  issn      = {0378-620X},
  doi       = {10.1007/s00020-014-2122-4},
  pages     = {577 -- 587},
  year      = {2014},
  abstract  = {In a recent paper, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes.},
  language  = {en}
}
@article{Wallenta2012,
  author    = {Wallenta, D.},
  title     = {Elliptic quasicomplexes on compact closed manifolds},
  series = {Integral equations and operator theor},
  volume    = {73},
  journal   = {Integral equations and operator theor},
  number    = {4},
  publisher = {Springer},
  address   = {Basel},
  issn      = {0378-620X},
  doi       = {10.1007/s00020-012-1983-7},
  pages     = {517 -- 536},
  year      = {2012},
  abstract  = {We consider quasicomplexes of pseudodifferential operators on a smooth compact manifold without boundary. To each quasicomplex we associate a complex of symbols. The quasicomplex is elliptic if this symbol complex is exact away from the zero section. We prove that elliptic quasicomplexes are Fredholm. Moreover, we introduce the Euler characteristic for elliptic quasicomplexes and prove a generalisation of the Atiyah-Singer index theorem.},
  language  = {en}
}
@article{Tarkhanov2011,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {The dirichlet to Neumann operator for elliptic complexes},
  series = {Transactions of the American Mathematical Society},
  volume    = {363},
  journal   = {Transactions of the American Mathematical Society},
  number    = {12},
  publisher = {American Mathematical Soc.},
  address   = {Providence},
  issn      = {0002-9947},
  pages     = {6421 -- 6437},
  year      = {2011},
  abstract  = {We define the Dirichlet to Neumann operator for an elliptic complex of first order differential operators on a compact Riemannian manifold with boundary. Under reasonable conditions the Betti numbers of the complex prove to be completely determined by the Dirichlet to Neumann operator on the boundary.},
  language  = {en}
}