Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds
Grzegorz Graff, Jerzy Jezierski · AIMS Press eBooks · 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 equalto the minimum of #Fix($g^r$) over all maps $g$ smoothly homotopic to $f$. Inthis paper we calculate the invariant $D^4_r [f]$ for the class of smooth self-mapsof 4-manifolds with fast grow of Lefschetz numbers and for $r$ being a productof di erent primes.