COMPUTATIONS OF THE LEAST NUMBER OF PERIODIC POINTS OF SMOOTH BOUNDARY-PRESERVING SELF-MAPS OF SIMPLY-CONNECTED MANIFOLDS

Let r be an odd natural number, M a compact simply-connected smooth manifold, dimM >= 4, such that its boundary partial derivative M is also simply-connected. We consider f, a C-1 self-maps of M, preserving partial derivative M. In [G. Graff and J. Jezierski, Geom. Dedicata 187 (2017), 241-258] the smooth Nielsen type periodic number D-r(f; M, partial derivative M) was defined and proved to be equal to the minimal number of r-periodic points for all maps preserving partial derivative M and C-1-homotopic to f. In this paper we demonstrate a purely combinatorial method of calculation of the invariant and illustrate it in various cases.