A new class of nonpositively-curved 3-manifolds
by
Jon McCammond
Texas A&M University
Coauthors: Murray Elder (Texas A&M), John Meier (Lafayette)

Thurston conjectured that a closed triangulated 3-manifold in which every edge degree is either 5 or 6 and no two edges of degree 5 lie in a common 2-cell, has a fundamental group which is word-hyperbolic. In this talk, I'll describe how we establish Thurston's conjecture by proving that such a triangulation admits a piecewise Euclidean metric of non-positive curvature with no isometrically embedded flat planes. The proof involves a mixture of computer computation and techniques from small-cancelation theory.

Date received: February 22, 2002