Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds
Grzegorz Graff - Department of Algebra, Faculty of Applied Physics and Mathematics, Gdansk University of Technology, ul. Narutowicza 11/12, 80-952 Gdansk, 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 $D^m_r [f]$ 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.
Keywords: Indices of iterations, smooth maps, Nielsen number
Received: July 2010; Revised: February 2011; Published: October 2011. |