Relationship between cyclic suspension and k-twist-spinning constructions

Identify and characterize explicit relationships between the cyclic suspension construction (including Thom–Sebastiani-type setups) and k-twist-spinning for fibered knots and links in odd-dimensional spheres, clarifying how these constructions correspond in terms of fibers, monodromies, and covering structures.

Background

The introduction reviews cyclic suspension (Thom–Sebastiani) constructions for fibered links and Zeeman’s k-twist-spinning for higher-dimensional knots, noting several parallel properties such as cyclic branched covering fibers and periodic monodromies.

Despite these similarities, the authors remark that no relationships are currently known connecting the two constructions. A precise correspondence, if it exists, could deepen understanding of fibered links across dimensions.

References

Properties of fibered knots obtained by a cyclic suspension and a $k$-twist-spinning are similar, though no relations between them are known yet.

— Twist spun knots of twist spun knots of classical knots (2409.00650 - Fukuda et al., 1 Sep 2024) in Introduction (Section 1)