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

Pages: 523 - 532, Issue Special, September 2011

 Abstract        Full Text (344.5K)              

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

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 $D^m_r [f]$ 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.

Keywords:  Indices of iterations, smooth maps, Nielsen number
Mathematics Subject Classification:  Primary: 37C25, 55M20; Secondary: 37C05

Received: July 2010;      Revised: February 2011;      Published: October 2011.