For more information about this meeting, contact Anatole Katok, Mari Royer, Yakov Pesin, Dmitri Burago.
|Title:||Geometric consequences of algebraic rank in hyperbolic $3$-manifolds|
|Seminar:||Center for Dynamics and Geometry Seminar|
|Speaker:||Ian Biringer, Yale|
|Mostow's rigidity theorem states that a closed hyperbolic $3$-manifold M is determined up to isometry by the algebra of its fundamental group. We will discuss how the geometry of M is constrained by the minimal number of elements needed to generate its fundamental group; this invariant is called the (algebraic) rank of M. In particular, we will explain how M can be decomposed into a number of geometric building blocks such that the complexities of the blocks and of the decomposition depend only on M's algebraic rank and on a lower bound for M's injectivity radius.
Our work links rank and injectivity radius to a number of other geometric invariants, including Heegaard genus, the Cheeger constant and the first eigenvalue of the Laplacian. One can also use the techniques involved to prove a finiteness statement for the number of commensurability classes of arithmetic closed hyperbolic $3$-manifolds with bounded rank and injectivity radius.
Joint with Juan Souto.|
Room Reservation Information
|Date:||03 / 31 / 2010|
|Time:||03:30pm - 05:30pm|