This Tuesday at 5:00, the seminar hosts Jeff Brock of Brown University.
Title: Fat, exhausted integer homology spheres
Abstract: Since Perelman’s groundbreaking proof of the geometrization conjecture for three-manifolds, the possibility of exploring tighter correspondences between geometric and algebraic invariants of three-manifolds has emerged. In this talk, we address the question of how homology interacts with hyperbolic geometry in 3-dimensions, providing examples of hyperbolic integer homology spheres that have large injectivity radius on most of their volume. (Indeed such examples can be produced that arise as -Dehn filling on knots in the three-sphere). Such examples fit into a conjectural framework of Bergeron, Venkatesh and others providing a counterweight to phenomena arising in the setting of arithmetic Kleinian groups. This is joint work with Nathan Dunfield.