On the BNSR invariants of link groups

Yuta Nozaki

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arXiv · 2606.02978

On the BNSR invariants of link groups

Yuta Nozaki

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Abstract

For a finitely generated group $G$, the Bieri-Neumann-Strebel-Renz (BNSR) invariants are subsets of the character sphere of $G$ that govern the finiteness properties of normal subgroups containing the commutator subgroup. We investigate the BNSR invariants of link groups and $2$-knot groups. In particular, for a link $L$ with at least two components, we prove that the commutator subgroup of the link group is finitely generated if and only if $L$ is a Hopf link. Moreover, we show that there exists a ribbon $2$-knot whose knot group has a non-symmetric BNS invariant.

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Yuta Nozaki. 2026-06-02. On the BNSR invariants of link groups. https://arxiv.org/abs/2606.02978

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