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.
|Number of pages||10|
|Journal||Osaka Journal of Mathematics|
|Publication status||Published - 2017 Oct|
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