A Nielsen type periodic number for maps over $B$

Abstract

Let $Y\to E\stackrel{p}{\to }B$ be a fibration and let $f:E\to E$ be a fiber map over $B$. In this work, we study the geometric and algebraic Reidemeister classes of the iterates of $f$ and introduce a Nielsen-type periodic number over $B$, denoted by $N_B{P}_n(f)$. When $B$ is a point, then $N_B{P}_n(f)$ coincides with the classical Nielsen periodic number.