Minimal number of periodic points for C 1 self-maps of compact simply-connected manifolds

Abstract

Let ƒ be a self-map of a smooth compact connected and simply-connected manifold of dimension m ≥ 3, r a fixed natural number. In this paper we define a topological invariant which is the best lower bound for the number of r-periodic points for all C1 maps homotopic to ƒ. In case m = 3 we give the formula for and calculate it for self-maps of S2 × I.