## 22 Citations

Finite Group Actions and 3-Manifold Topology

- Mathematics
- 2004

This article provides a brief sketch of the theory of ̄nite group actions studied in terms of 3-manifold topology. We will survey the results in the geometric case and equivariant techniques in…

SURGERIES ON SMALL VOLUME HYPERBOLIC 3-ORBIFOLDS

- Mathematics
- 2001

The computer program SnapPea by J. Weeks is a powerful tool for calculating the volumes of hyperbolic 3-manifolds. The small volume hyperbolic 3-manifolds have been studied rather intensively. The…

Surgery on Small Volume Hyperbolic 3-Orbifolds

- Mathematics
- 2001

The computer program SnapPea by J. Weeks is a powerful tool for calculating the volumes of hyperbolic 3-manifolds. The small volume hyperbolic 3-manifolds have been studied rather intensively. The…

Hurwitz groups, maximal reducible groups and maximal handlebody groups

- Mathematics
- 2021

. A Hurwitz group is a ﬁnite group of orientation-preserving diﬀeomorphisms of maximal possible order 84( g − 1) of a closed orientable surface of genus g > 1. A maximal handlebody group instead is a…

Equivariant Heegaard genus of reducible 3-manifolds

- Mathematics
- 2020

The equivariant Heegaard genus of a 3-manifold $M$ with the action of a finite group $G$ of diffeomorphisms is the smallest genus of an equivariant Heegaard surface for $M$. Although a Heegaard…

Tetrahedral Coxeter groups, large group-actions on 3-manifolds and equivariant Heegaard splittings

- Mathematics
- 2020

We consider finite group-actions on closed, orientable and nonorientable 3-manifolds M which preserve the two handlebodies of a Heegaard splitting of M of some genus g > 1 (maybe interchanging the…

On large orientation-reversing finite group-actions on 3-manifolds and equivariant Heegaard decompositions

- MathematicsMonatshefte für Mathematik
- 2019

We consider finite group-actions on closed, orientable and nonorientable 3-manifolds; such a finite group-action leaves invariant the two handlebodies of a Heegaard splitting of M of some genus g .…

Equivariant hyperbolization of $3$-manifolds via homology cobordisms

- Mathematics
- 2018

The main result of this paper is that any $3$-dimensional manifold with a finite group action is equivariantly, invertibly homology cobordant to a hyperbolic manifold; this result holds with suitable…

Maximum orders of cyclic and abelian extendable actions on surfaces

- Mathematics
- 2013

Let $\Sigma_g (g>1)$ be a closed surface embedded in $S^3$. If a group $G$ can acts on the pair $(S^3, \Sigma_g)$, then we call such a group action on $\Sigma_g$ extendable over $S^3$.
In this paper…