# American Institute of Mathematical Sciences

2011, 2011(Special): 523-532. doi: 10.3934/proc.2011.2011.523

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

 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, Poland

Received  July 2010 Revised  February 2011 Published  October 2011

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 $D^m_r [f]$ de fined 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 di erent primes.
Citation: Grzegorz Graff, Jerzy Jezierski. Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds. Conference Publications, 2011, 2011 (Special) : 523-532. doi: 10.3934/proc.2011.2011.523
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