Let f be a continuous self-map of a smooth compact connected and simply-connected manifold of dimension m ≥ 3 and r a fixed natural number. A topological invariant , introduced by the authors [Forum Math. 21 (2009)], is equal to the minimal number of r-periodic points for all smooth maps homotopic to f. In this paper we calculate for all self-maps of S³.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-2-3,
author = {Grzegorz Graff and Jerzy Jezierski},
title = {Minimal number of periodic points for smooth self-maps of S$^3$},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {127-144},
zbl = {1184.37017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-2-3}
}
Grzegorz Graff; Jerzy Jezierski. Minimal number of periodic points for smooth self-maps of S³. Fundamenta Mathematicae, Tome 205 (2009) pp. 127-144. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-2-3/