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

J. A. Hillman

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

Geometric Topology 2023-07-21 v2

Authors: J. A. Hillman

Abstract

We reconsider work of Elkalla on subnormal subgroups of 3-manifold groups, giving essentially algebraic arguments that extend to the case of $PD_3$ -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.

Cite

@article{arxiv.2106.15750,
  title  = {Subnormality in $PD_3$-groups and $L^2$-Betti numbers},
  author = {J. A. Hillman},
  journal= {arXiv preprint arXiv:2106.15750},
  year   = {2023}
}

Comments

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

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