Kyungpook Mathematical Journal 2009; 49(1): 7-14
Published online March 23, 2009
Copyright © Kyungpook Mathematical Journal.
Representations of the Braid Group and Punctured Torus Bundles
1Department of Mathematics, Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho, Koganei, Tokyo 184-8588, Japan
2Department of Mathematics, Akita University, 1-1 Tegata-Gakuenmachi, Akita 0108502, Japan
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.
Keywords: representation, braid group, punctured torus bundle, Dehn filling