Daniel Berend

The class of concentrated periodic diffeomorphisms g: M → M is introduced. Adiffeomorphism is called concentrated if, roughly speaking, its normal eigenvalues range in a small(with respect to the period of g and the dimension of M) arc on the circle. In many ways, the cyclic action generated by such a g behaveson the one hand as a circle action and on the other hand as a generic prime power order cyclic action. For example, as for circle actions, Sign(g, M) = Sign(M^g), provided that the left-hand side is an integer; as for prime power order actions, g cannot have asingle fixed point if M is closed. A variety of integrality results, relating to the usual signatures of certain characteristic submanifolds of the regularneighbourhood of M^g in M to Sign(g, M) via thenormal g-representations, is established.