Reducing the number of periodic points in the smooth homotopy class of a self-map of a simply-connected manifold with periodic sequence of Lefschetz numbers

Grzegorz Graff, and Agnieszka Kaczkowska. "Reducing the number of periodic points in the smooth homotopy class of a self-map of a simply-connected manifold with periodic sequence of Lefschetz numbers." Annales Polonici Mathematici 107.1 (2013): 29-48. <http://eudml.org/doc/286318>.

@article{GrzegorzGraff2013,
abstract = {Let f be a smooth self-map of an m-dimensional (m ≥ 4) closed connected and simply-connected manifold such that the sequence $\{L(fⁿ)\}_\{n=1\}^\{∞\}$ of the Lefschetz numbers of its iterations is periodic. For a fixed natural r we wish to minimize, in the smooth homotopy class, the number of periodic points with periods less than or equal to r. The resulting number is given by a topological invariant J[f] which is defined in combinatorial terms and is constant for all sufficiently large r. We compute J[f] for self-maps of some manifolds with simple structure of homology groups.},
author = {Grzegorz Graff, Agnieszka Kaczkowska},
journal = {Annales Polonici Mathematici},
keywords = {minimal number of periodic points; Nielsen number; fixed point index; smooth map},
language = {eng},
number = {1},
pages = {29-48},
title = {Reducing the number of periodic points in the smooth homotopy class of a self-map of a simply-connected manifold with periodic sequence of Lefschetz numbers},
url = {http://eudml.org/doc/286318},
volume = {107},
year = {2013},
}

TY - JOUR
AU - Grzegorz Graff
AU - Agnieszka Kaczkowska
TI - Reducing the number of periodic points in the smooth homotopy class of a self-map of a simply-connected manifold with periodic sequence of Lefschetz numbers
JO - Annales Polonici Mathematici
PY - 2013
VL - 107
IS - 1
SP - 29
EP - 48
AB - Let f be a smooth self-map of an m-dimensional (m ≥ 4) closed connected and simply-connected manifold such that the sequence ${L(fⁿ)}_{n=1}^{∞}$ of the Lefschetz numbers of its iterations is periodic. For a fixed natural r we wish to minimize, in the smooth homotopy class, the number of periodic points with periods less than or equal to r. The resulting number is given by a topological invariant J[f] which is defined in combinatorial terms and is constant for all sufficiently large r. We compute J[f] for self-maps of some manifolds with simple structure of homology groups.
LA - eng
KW - minimal number of periodic points; Nielsen number; fixed point index; smooth map
UR - http://eudml.org/doc/286318
ER -