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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Pure Maths Colloquium: Punctured torus groups and 2-bridge knots

Presented by "Makoto Sakuma (Osaka University, Japan)",

6 May 2002 00:00 in CM221

" A punctured torus group is a discrete free subgroup of PSL(2,C) generated by two transformations A and B such
that the commutator [A,B] is parabolic. In his famous unpublished work, Troels Jorgensen gave a beautiful description
of the Ford fundamental domain of (quasifuchsian) punctured torus groups. In this talk, I will present a generalization
of his result to the groups on the outside of the space of quasifuchsian punctured torus groups. To be precise, we show
that each group in the natural extension of rational pleating varieties of the quasifuchsian punctured torus space is the
holonomy group of a hyperbolic cone manifold whose Ford fundamental domain can be explicitly described. This
enables us to explicitly construct the hyperbolic structures and the Epstein-Penner decompositions of the 2-bridge knot
complements. As an application to knot theory, we recover the classification theorem of the 2-bridge knots due to Schubert
and the calculation of the outer automorphism groups of 2-bridge knot groups due to Conway and Bonahon-Siebenmann
(both unpublished). This is joint work with Hirotaka Akiyoshi, Masaaki Wada and Yasushi Yamashita."

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