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Computations of the least number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
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.
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Authors (3)
-
Jerzy Jezierski
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
-
Topological Methods in Nonlinear Analysis
no. 56,
pages 589 - 606,
ISSN: 1230-3429 - Language:
- English
- Publication year:
- 2020
- Bibliographic description:
- Graff G., Jezierski J., Myszkowski A.: Computations of the least number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds// Topological Methods in Nonlinear Analysis -Vol. 56,iss. 2 (2020), s.589-606
- DOI:
- Digital Object Identifier (open in new tab) 10.12775/tmna.2020.035
- Sources of funding:
- Verified by:
- Gdańsk University of Technology
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