TOPOLOGY SEMINAR
4/7/2005
Jeff Brock
Brown University
Heegaard splittings, pants decompositions of
surfaces, and volumes of hyperbolic 3-manifolds.
The combinatorics of simple closed curves on surfaces play integrally into the study of Heegaard splittings of 3-manifolds, where they serve to indicate a kind of complexity; Hempel explored the relation of Heegaard splittings to the complex of curves, eliciting necessary conditions for the existence a hyperbolic structure. When M is assumed hyperbolic, one can explore relations between combinatorics of curves and the geometry of the 3-manifold. In joint work with Juan Souto, we establish that a related complexity arising
from pants decompositions of surfaces serves to estimate the volume of M, echoing earlier results for 3-manifolds fibering over the circle.