The groups of branched twist-spun knots

Jonathan A. Hillman

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 \(PD_3\)-groups. We show also that each group is the group of at most finitely many branched twist spins.

Keywords: cyclic branched cover, group, knot, twist spin.

AMS Subject Classification: Primary 57Q45.