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.