A natural number m is called the homotopy minimal period of a map f : X → X if it is a minimal period for every map g homotopic to f. In this paper we show that the complete description of the sets of homotopy minimal periods of a torus map given by Jiang and Llibre extends to the case of a map of compact nilmanifold. The proof follows the approach of Jiang and Llibre and uses the Nielsen theory. The main geometric ingredient is a theorem on cancelling m-periodic points of a local homeomorphism. For a map of nilmanifold the general case reduces to it by a homotopy argument. (2000): 55M20, 57N05, 54H25
Mathematics Subject Classification
Let f be a self-map of a smooth compact connected and simplyconnected manifold of dimension m ≥ 3, r a fixed natural number. In this paper we define a topological invariant D m r [f ] which is the best lower bound for the number of r-periodic points for all C 1 maps homotopic to f . In case m = 3 we give the formula for D 3 r [f ] and calculate it for self-maps of S 2 × I.2000 Mathematics Subject Classification. Primary 37C25, 55M20 Secondary 37C05.
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