Higher dimensional algebraic fiberings of group extensions

TL;DR

This paper investigates conditions under which group extensions admit higher-dimensional algebraic fibering, leading to insights on group incoherence and examples involving pure braid groups and poly-surface groups.

Contribution

It establishes new criteria for higher-dimensional algebraic fibering of group extensions and provides geometric examples involving complex projective varieties.

Findings

Conditions for higher-dimensional algebraic fibering established

Examples of groups with algebraic fibers of type F_n but not FP_{n+1}

Applications to pure braid groups and poly-surface groups

Abstract

We prove some conditions for the existence of higher dimensional algebraic fibering of group extensions. This leads to various corollaries on incoherence of groups and some geometric examples of algebraic fibers of type $F_n$ but not $FP_{n+1}$ of some groups including pure braid groups and families of poly-surface groups that are fundamental groups of complex projective varieties.