• Corpus ID: 244773260

Generalized torsion for hyperbolic $3$--manifold groups with arbitrary large rank

@inproceedings{Ito2021GeneralizedTF,
  title={Generalized torsion for hyperbolic \$3\$--manifold groups with arbitrary large rank},
  author={Tetsuya Ito and Kimihiko Motegi and Masakazu Teragaito},
  year={2021}
}
Let G be a group and g a non-trivial element in G. If some nonempty finite product of conjugates of g equals to the trivial element, then g is called a generalized torsion element. To the best of our knowledge, we have no hyperbolic 3–manifold groups with generalized torsion elements whose rank is explicitly known to be greater than two. The aim of this short note is to demonstrate that for a given integer n > 1 there are infinitely many closed hyperbolic 3–manifolds Mn which enjoy the property… 

Figures from this paper

References

SHOWING 1-10 OF 21 REFERENCES
Generalized torsion and decomposition of 3–manifolds
A nontrivial element in a group is a generalized torsion element if some nonempty finite product of its conjugates is the identity. We prove that any generalized torsion element in a free product of
Generalized torsion for knots with arbitrarily high genus
Let G be a group and let g be a non-trivial element in G. If some non-empty finite product of conjugates of g equals to the identity, then g is called a generalized torsion element. We say that a
Generalized torsion elements and hyperbolic links
In a group, a generalized torsion element is a non-identity element whose some non-empty finite product of its conjugates yields the identity. Such an element is an obstruction for a group to be
Generalized Torsion in Knot Groups
Abstract In a group, a nonidentity element is called a generalized torsion element if some product of its conjugates equals the identity. We show that for many classical knots one can ûnd generalized
Three dimensional manifolds, Kleinian groups and hyperbolic geometry
1. A conjectural picture of 3-manifolds. A major thrust of mathematics in the late 19th century, in which Poincare had a large role, was the uniformization theory for Riemann surfaces: that every
Dehn surgery on arborescent knots
A knot K is called an arborescent knot if it can be obtained by summing and gluing several rational tangles together, see [7] or below for more detailed definitions. Recall that a 3-manifold is
Generalized torsion elements in the knot groups of twist knots
It is well known that any knot group is torsion-free, but it may admit a generalized torsion element. We show that the knot group of any negative twist knot admits a generalized torsion element. This
Alexander polynomial obstruction of bi-orderability for rationally homologically fibered knot groups
We show that if the fundamental group of the complement of a rationally homologically fibered knot in a rational homology 3-sphere is bi-orderable, then its Alexander polynomial has at least one
On Heegaard decompositions of torus knot exteriors and related Seifert fibre spaces
The Heegaard decompositions of genus 2 oftorus knot exteriors are classified with respect to homeomorphisms. It turns out that in general there are three different classes which are also the isotopy
...
...