Abstract
Let $r$ be an odd natural number, $M$ a compact simply-connected smooth manifold, $\dim M\geq 4$, such that its boundary $\partial M$ is also simply-connected. We consider $f$, a $C^1$ self-maps of $M$, preserving $\partial M$. In [G. Graff and J. Jezierski, Geom. Dedicata 187 (2017), 241-258] the smooth Nielsen type periodic number $D_r(f;M,\partial M)$ was defined and proved to be equal to the minimal number of $r$-periodic points for all maps preserving $\partial M$ 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.
Citation
Grzegorz Graff. Jerzy Jezierski. Adrian Myszkowski. "Computations of the least number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds." Topol. Methods Nonlinear Anal. 56 (2) 589 - 606, 2020. https://doi.org/10.12775/TMNA.2020.035
Information