Boundary reduction of spectral invariants. -- Results and puzzles (Q2702371)

The author studies various cases of boundary reduction of spectral invariants which are related to the index, to the spectral flow, and to the \(\zeta\) regularized determinant for Dirac operators or families of Dirac operators on a compact manifold with boundary. These relate to genuine boundary reductions where a global invariant can be recovered from information on the boundary, correction formulae where the difference between two spectral invariants localizes at the boundary, and pasting formulae where a global invariant on a partitioned manifold can be decomposed into components on each partition plus a correction along the splitting hypersurface. NEWLINENEWLINENEWLINESection 1 reviews general restriction results for Dirac operators. Sections 2-3 deal with the index and the spectral flow. Section 4 deals with the determinant as used in quantum field theories.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00049].