Homological properties of periodic homeomorphisms of 4-manifolds (Q1117511)

This paper shows that certain homological results are valid for periodic homeomorphisms of four dimensional manifolds even though they are not more generally. The first example is: Theorem. If f: \(M^ 4\to M^ 4\) is a periodic homeomorphism of a closed four dimensional manifold, then the Lefschetz number of f is the Euler characteristic of the fixed point set of f. The other examples given concern the ideal class invariant \(\alpha\) (M,f)\(\in \tilde K_ 0(Z[Z_ p])\) for a homeomorphism f of odd prime period p on a closed simply connected four manifold. The results say that \(\alpha (M,f)=0\) if f is locally linear, and more generally \(\alpha\) (M,f) can be any invariant of the canonical conjugation.