51 Mathematik
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510 Mathematik
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In paper (Flad and Harutyunyan in Discrete Contin Dyn Syst 420-429, 2011) is shown that the Hamiltonian of the helium atom in the Born-Oppenheimer approximation, in the case if two particles coincide, is an edge-degenerate operator, which is elliptic in the corresponding edge calculus. The aim of this paper is an analogous investigation in the case if all three particles coincide. More precisely, we show that the Hamiltonian in the mentioned case is a corner-degenerate operator, which is elliptic as an operator in the corner analysis.
We construct eta- and rho-invariants for Dirac operators, on the universal covering of a closed manifold, that are invariant under the projective action associated to a 2-cocycle of the fundamental group. We prove an Atiyah-Patodi-Singer index theorem in this setting, as well as its higher generalisation. Applications concern the classification of positive scalar curvature metrics on closed spin manifolds. We also investigate the properties of these twisted invariants for the signature operator and the relation to the higher invariants.
