Equivariant method for periodic maps

Abstract:

The notion of coherency with submanifolds for a Morse function on a manifold is introduced and discussed in a general way. A Morse inequality for a given periodic transformation which compares the invariants called qth Euler numbers on fixed point set and the invariants called qth Lefschetz numbers of the transformations is thus obtained. This gives a fixed point theorem in terms of qth Lefschetz number for arbitrary q.