The groups of branched twist-spun knots

Abstract

We characterize the groups of branched twist spins of classical knots in terms of 3-manifold groups, and also give a purely algebraic, conjectural characterization in terms of $P{D}_3$-groups. We show also that each group is the group of at most finitely many branched twist spins.

arXiv commentv2: Introduction rewritten, new Theorem 8 and Corollary inserted. v3: New Theorem 10 and Corollary inserted. v4 paragraph before Theorem 4 rewritten