Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds

Grzegorz Graff; Jerzy Jezierski

doi:10.3934/proc.2011.2011.523

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2011, Volume 2011: 523-532. Doi: 10.3934/proc.2011.2011.523 open access

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Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds

Grzegorz Graff^1, and
Jerzy Jezierski^2,

1.
Department of Algebra, Faculty of Applied Physics and Mathematics, Gdansk University of Technology, ul. Narutowicza 11/12, 80-952 Gdansk
2.
Institute of Applications of Mathematics, Warsaw University of Life Sciences (SGGW), Nowoursynowska 159, 00-757 Warsaw

Received: July 2010

Revised: February 2011

Published: August 2017

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Abstract

Let $M$ be a smooth closed simply-connected $m$-dimensional manifold, $f$ be a smooth self-map of $M$ and $r$ be a given natural number. The invariant $D^m_r [f]$ defined by the authors in [Forum Math. 21 (2009)] is equal to the minimum of #Fix($g^r$) over all maps $g$ smoothly homotopic to $f$. In this paper we calculate the invariant $D^4_r [f]$ for the class of smooth self-maps of 4-manifolds with fast grow of Lefschetz numbers and for $r$ being a product of dierent primes.

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Mathematics Subject Classification: Primary: 37C25, 55M20; Secondary: 37C05.

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Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds

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