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4:00 pm Thursday, March 7, 2013 Colloquium: Fat, exhausted, integer homology spheresby Jeff Brock (Brown) in HB 227- Perelman's groundbreaking proof of the geometrization conjecture for three-manifolds has foregrounded the problem of exploring tighter correspondences between geometric and algebraic invariants of three-manifolds. 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 (1,n)-Dehn filling on knots in the three-sphere). Such examples fit into a conjectural framework of Bergeron, Venkatesh and others and provide a counterweight to phenomena arising in asymptotic L^2 invariants of families of covers of hyperbolic manifolds. This is joint work with Nathan Dunfield.
Submitted by jtanis@rice.edu |