Colloquium: Russell Ricks (Binghampton University)

Title: A Rank Rigidity Result for Certain Nonpositively Curved Spaces via Spherical Geometry

Abstract: To understand the geometry of nonpositively curved (NPC) spaces, it is natural to classify the various types of spaces that can occur. The Rank Rigidity Theorem for closed NPC manifolds separates the class of closed NPC manifolds into three very distinct types, and proves that nothing else can exist.

A version of Rank Rigidity has been conjectured for more general NPC spaces (CAT(0) spaces). In this talk, we discuss some progress toward the general conjecture, by reducing the problem to looking at patterns on spheres in the boundary at infinity. In particular, we can prove the conjecture for certain NPC spaces with one-dimensional boundary. In contrast to previous rank rigidity results, we do not assume any additional structure (such as a polyhedral or manifold structure) on the space.

Date: Tuesday, February 13
Time: 4:00 PM
Room: 135 TMCB