On the BNSR invariants of $2$-knot groups

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 $2$-knot groups and link groups. As an application, we prove Yasuda's conjecture that every non-trivial $2$-plat $2$-knot is non-fibered.

arXiv comment11 pages, 1 figure