Generalized torsion and Dehn filling

TL;DR

This paper constructs a generalized torsion element in the fundamental group of a 3-manifold obtained via Dehn surgery on a knot in the 3-sphere, advancing understanding of algebraic properties in 3-manifold groups.

Contribution

It introduces the first explicit construction of a generalized torsion element in the fundamental group resulting from Dehn surgery on a knot in S^3.

Findings

Existence of generalized torsion elements in certain 3-manifold groups

Explicit construction method for these elements

Implications for the algebraic structure of 3-manifold groups

Abstract

A generalized torsion element is a non-trivial element such that some non-empty finite product of its conjugates is the identity. We construct a generalized torsion element of the fundamental group of a 3-manifold obtained by Dehn surgery along a knot in the 3-sphere.