$PD_4$-complexes with $Ï_2$ a projective $\mathbb{Z}[Ï_1]$-module

Jonathan A. Hillman

paper

$P D_{4}$ -complexes with $I ¨ _{2}$ a projective $Z [I ¨ _{1}]$ -module

arXiv:2606.29356

Abstract

Let $X$ be a $P D_{4}$ -complex and let $I ¨ = I ¨ _{1} (X)$ . If $I ¨ $ is torsion-free and $I ¨ _{2} (X)$ is a finitely generated projective $Z [I ¨ ]$ -module then either $I ¨ $ is free or $I ¨ $ is $F P$ and $c . d . I ¨ = 4$ . If, moreover, $H^{3} (I ¨ ; Z [I ¨ ]) = 0$ then $I ¨ $ is a free product of $P D_{4}$ -groups and a free group.

PD4​-complexes with I¨2​ a projective Z[I¨1​]-module

Abstract

$P D_{4}$ -complexes with $I ¨ _{2}$ a projective $Z [I ¨ _{1}]$ -module