David Gabai
Princeton University, USA
July 2, 2012
Volumes of hyperbolic 3-manifolds: As part of his revolutionary work on hyperbolic geometry in the 1970's, Thurston generalizing work of Jorgensen and Gromov, showed that that the set of volumes of complete finite volume hyperbolic 3-manifolds is closed and well ordered. Recently, Robert Meyerhoff and Peter Milley and the speaker showed that the Weeks manifold is the unique lowest volume closed orientable one, culminating a 30+ year effort by many mathematicians using a wide variety of geometric and topological techniques. This lecture will survey these and other developments and discuss some of the many open problems in the area.
Princeton University, USA
July 2, 2012
Volumes of hyperbolic 3-manifolds: As part of his revolutionary work on hyperbolic geometry in the 1970's, Thurston generalizing work of Jorgensen and Gromov, showed that that the set of volumes of complete finite volume hyperbolic 3-manifolds is closed and well ordered. Recently, Robert Meyerhoff and Peter Milley and the speaker showed that the Weeks manifold is the unique lowest volume closed orientable one, culminating a 30+ year effort by many mathematicians using a wide variety of geometric and topological techniques. This lecture will survey these and other developments and discuss some of the many open problems in the area.