4/20/2006

Robert Meyerhoff
IAS and Boston College

Mom Technology and Low-Volume Hyperbolic 3- Manifolds

In the late 1970's, W. Thurston proved that the set of volumes of complete hyperbolic 3-manifolds (of finite volume) is well-ordered and of order type omega^omega. In particular, there is a smallest volume v(1), a second smallest volume v(2), and so on; and that this sequence v(1) < v(2) < v(3) < ... has a limit point v(omega) which is the smallest volume of a one-cusped hyperbolic 3-manifold. And so on after that.  D. Gabai, P. Milley, and I have developed a new method, the "Mom technology," which holds considerable promise for finding a reasonable collection of parent manifolds from which the low-volume manifolds can be obtained by hyperbolic Dehn surgery.