Seifert fibred knot manifolds

TL;DR

This paper investigates the conditions under which certain Seifert fibred knot manifolds are obtained via elementary surgery, introduces a new family of 2-knots with specific algebraic properties, and notes the absence of higher-dimensional examples.

Contribution

It identifies a new family of 2-knots with torsion-free, solvable groups, expanding the understanding of Seifert fibred knot manifolds in low dimensions.

Findings

Discovered a new family of 2-knots with torsion-free, solvable groups

Analyzed the classical case of elementary surgery on n-knot Seifert fibred manifolds

Found no higher-dimensional examples of such knots

Abstract

We consider the question of when is the closed manifold obtained by elementary surgery on an $n$-knot Seifert fibred over a 2-orbifold. After some observations on the classical case, we concentrate on the cases n=2 and 3. We have found a new family of 2-knots with torsion-free, solvable group, overlooked in earlier work. We know of no higher dimensional examples.