The involutions of compact symmetric spaces. IV (Q1304942)

This paper discusses and determines the signature \(\tau(M)\) and the \(g\)-signature \(g-\tau(M)\) of every compact oriented symmetric space \(M\) as well as the self-intersections \(SI(N;M)\) of subspaces \(N\) in \(M\) which are related to \(g-\tau(M)\) by the \(g\)-signature theorem or the generalized Lefschetz fixed point theorem of Atiyah-Singer in case \(g\) is an orientation-preserving involution of \(M\). In addition, a geometric application is given, as an example.