Resumen de On H-spaces over a base space

Hans Scheerer

• Working in the category of $k$-spaces we study the question when the group of vertical homotopy classes $\pi_0(SEC(B,E))$ of sections of a group-like space $E\rightarrow B$ over $B$ is nilpotent. As an application we obtain e.g. that the group of homotopy classes of fibre homotopy equivalences of a fibration $X\rightarrow B$ inducing the indentity on $H_\ast(X_b;\mathbb{Z})$ is nilpotent, if $B$ as a connected finite- dimensional and the fibre $X_b$ is a connected nilpotent finite-dimensional $CW$-complex.\newline\newline KEY WORDS: $H$-spaces over a base space, fibre homotopy equivalence, spaces of sections.