Counting hyperbolic 3-manifolds with a given volume

Craig Hodgson

University of Melbourne

Brandeis University

Thursday, March 22, 2012

Talk at 4:30 p.m. in 317 Goldsmith Hall

Tea at 4:00 p.m. in 300 Goldsmith Hall

Abstract: We will begin with a brief introduction to hyperbolic 3-manifolds and their volumes. Thurston and Jorgensen showed that there is a finite number N(v) of hyperbolic 3-manifolds with any given volume v. We will look at the question of how N(v) varies with v.

We show that there is an infinite sequence of closed hyperbolic 3-manifolds that are uniquely determined by their volumes. The proof uses work of Neumann-Zagier on the change in volume during hyperbolic Dehn surgery together with some elementary number theory.

We also describe examples showing that the number of hyperbolic link complements with volume v can grow at least exponentially fast with v.

(This is joint work with Hidetoshi Masai, Tokyo Institute of Technology)

Home Web page: Alexandru I. Suciu Posted: March 19, 2012
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