Colloquium: Tam Nguyen Phan (Binghamton U.)

When:
March 8, 2017 @ 3:30 pm – 4:30 pm
2017-03-08T15:30:00-10:00
2017-03-08T16:30:00-10:00
Where:
Keller 401

Speaker: Tam Nguyen Phan (Binghamton U.)

Title: Examples of negatively curved and nonpositively curved manifolds

Abstract: Let M be a noncompact, complete, Riemannian manifold. Gromov proved that if the sectional curvature of M negative and bounded, and if the volume of M is finite, then M is homeomorphic to the interior of a compact manifold overline{M} with boundary B. In other words, M has finitely many ends, and each end of M is topologically a product of a closed manifold C with a ray. A natural question is how the geometry (i.e. in terms of the curvature) of M controls the topology of C. The same question is interesting in nonpositive curvature settings. I will discuss what topological restrictions there are on each end and give old and new constructions of such manifolds.