BNS INVARIANTS AND ALGEBRAIC FIBRATIONS OF GROUP EXTENSIONS

Abstract Let G be a finitely generated group that can written as an extension $$ \begin{align*} 1 \longrightarrow K \stackrel{i}{\longrightarrow} \stackrel{f}{\longrightarrow} \Gamma \end{align*} where is group. By study of the Bieri–Neumann–Strebel (BNS) invariants we prove if $b_1(G)> b_1(\Gamma ) > 0$ , then algebraically fibres; is, admits epimorphism to $\Bbb {Z}$ with kernel. An interesting case this occurrence when fundamental surface bundle over $F \hookrightarrow X \rightarrow B$ Albanese dimension $a(X) = 2$ . As application, show has virtual $va(X) and base fibre have genus greater $1$ noncoherent. This answers for broad class bundles question J. Hillman ([9, Question 11(4)]). Finally, there exist whose BNS structure differs from Kodaira fibrations, determined by T. Delzant.