Branched twist spins and knot determinants

2016/04/29 by Mizuki Fukuda, Fukuda, Mizuki · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.1604.08828

openalex publication_date 2016/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Irreducible SL(2,ℂ)-metabelian representations of branched twist spins

Related

• Distinguishing 2-knots admitting circle actions by fundamental groups
• The groups of branched twist-spun knots
• Gluck twists along 2-knots with periodic monodromy
• Representations of branched twist spins with a non-trivial center of order 2
• Branched covers of twist-roll spun knots and turned twisted tori