Subnormality in $PD_3$-groups and $L^2$-Betti numbers

J. A. Hillman

paper

Subnormality in $P D_{3}$ -groups and $L^{2}$ -Betti numbers

arXiv:2106.15750

Abstract

We reconsider work of Elkalla on subnormal subgroups of 3-manifold groups, giving essentially algebraic arguments that extend to the case of $P D_{3}$ -groups and group pairs. However the argument relies on an $L^{2}$ -Betti number hypothesis which has not yet been shown to hold in general.

v2. New Corollary 9 and \S6, based on recent work by P.SŚanchez-Peralta (arXiv: 2307.07031 [math.GR])

Subnormality in PD3​-groups and L2-Betti numbers

Abstract

Subnormality in $P D_{3}$ -groups and $L^{2}$ -Betti numbers