Homotopy minimal periods for fiber maps on $S^{1}$-bundles over $S^{1}$

Abstract

Given $Y \to M \stackrel{p}{\to} B$ a fiber bundle and $f: M \to M$ a fiber map over $B$, we introduce the definition of homotopy minimal periods for $f$ denoted by $H_{B}Per(f).$ In the case where $M$ is a fiber bundle with base and fiber $S^{1}$ we presented a complete description of $H_{S^{1}}Per(f).$