Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Drew Sills**, Rutgers University, asills {at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: A random tunnel number one 3-manifold does not fiber over the circle

Speaker: **Dylan Thurston**, Columbia University (Barnard College)

Date: Thursday, October 26, 2006 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

There are two natural notions of "random" for tunnel number one 3-manifolds (that is, a manifold obtained by attaching a disk to a genus 2 handlebody). With respect to both notions of random, experiments show that a random manifold does not fiber over S^1 when the manifold is large enough. We prove it with respect to one notion. The question is motivated by the virtual fibration conjecture. We use techniques of Brown to turn the question into a group theory question and techniques of Agol, Hass, and W. Thurston to study the question for such large manifolds. This is joint work with Nathan Dunfield.