ABSTRACT
This appendix deals with the spectral η-invariant of Atiyah, Patodi and Singer (1975) and its generalization given by Melrose (1995). This invariant is almost as fundamental in elliptic theory as the index. It appears in many index formulas, while its applications range from algebraic geometry (Atiyah, Donnelly and Singer 1983) to quantum field theory (Witten 1985). The study of the η-invariant in this appendix is based on the paper by Seeley (1967) (see also Grubb and Seeley 1996). A detailed exposition of the η-invariant can be found in the monographs by Gilkey (1995, 1989a) and Booß-Bavnbek and Wojciechowski (1993). The η-invariant of parameter-dependent elliptic operators was subsequently studied and generalized by Lesch and Pflaum (2000), Nistor (2002), and Moroianu (2003).
