Periodic points of equivariant maps
Authors:
- Jerzy Jezierski,
- Wacław Bolesław Marzantowicz
Abstract
We assume that X is a compact connected polyhedron, G is a finite group acting freely on X, and f: X → X an G-equivariant map. We find formulae for the least number of n-periodic points in the equivariant homotopy class of f, i.e., inf
h
# Fix(h
n
) (where h is G-homotopic to f). As an application we prove that the set of periodic points of an equivariant map is infinite provided the action on the rational homology of X is trivial and the Lefschetz number L(f
n
) does not vanish for infinitely many indices n commeasurable with the order of G. Moreover, at least linear growth, in n, of the number of points of period n is shown.
- Record ID
- UAMe0140409a54046bda1a66ef770adb2f6
- Author
- Journal series
- Mathematica Scandinavica, ISSN 0025-5521
- Issue year
- 2010
- Vol
- 107
- Pages
- 224-248
- ASJC Classification
- Language
- (en) English
- Score (nominal)
- 0
- Score source
- journalList
- Publication indicators
- = 1; = 1; : 2010 = 0.757; : 2010 (2 years) = 0.356 - 2010 (5 years) =0.520
- Uniform Resource Identifier
- https://researchportal.amu.edu.pl/info/article/UAMe0140409a54046bda1a66ef770adb2f6/
- URN
urn:amu-prod:UAMe0140409a54046bda1a66ef770adb2f6
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