Abstract
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.
Original language | English |
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Pages (from-to) | 679-688 |
Number of pages | 10 |
Journal | Osaka Journal of Mathematics |
Volume | 54 |
Issue number | 4 |
Publication status | Published - 2017 Oct |
Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)