A branched twist spin is a generalization of twist spun knots, which appeared
in the study of locally smooth circle actions on the 4-sphere due to
Montgomery, Yang, Fintushel and Pao. In this paper, we give a sufficient
condition to distinguish non-equivalent, non-trivial branched twist spins by
using knot determinants. To prove the assertion, we give a presentation of the
fundamental group of the complement of a branched twist spin, which generalizes
a presentation of Plotnick, calculate the first elementary ideals and obtain
the condition of the knot determinants by substituting −1 for the
indeterminate.Comment: 10 pages, 4 figure
