• 대한수학회보
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• 제59권2호
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• pp.351-360
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• 2022

We prove that a punctured-torus group of hyperbolic 4-space which keeps an embedded hyperbolic 2-plane invariant has a strictly parabolic commutator. More generally, this rigidity persists for a punctured-surface group.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권1호
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• pp.73-88
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• 2004

A punctured torus $\Sigma(1,1)$ is a building block of oriented surfaces. The goal of this paper is to formulate the matrix presentations of elements of the Teichmuller space of a punctured torus. Let $\cal{C}$ be a matrix presentation of the boundary component of $\Sigma(1,1)$.In the level of the matrix group $\mathbb{SL}$($\mathbb2,R$) we shall show that the trace of $\cal{C}$ is always negative.

• Kyungpook Mathematical Journal
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• 제49권1호
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• pp.7-14
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• 2009

In this short note, we consider a family of linear representations of the braid group and the fundamental group of a punctured torus bundle over the circle. We construct an irreducible (special) unitary representation of the fundamental group of a closed 3-manifold obtained by the Dehn filling.