Montreal Geometric & Combinatorial Group Theory Seminar

Speaker: Dani Wise (McGill)

Title: “Sectional Curvature, Compact Cores, and Local Quasiconvexity”

Date: 3:30pm Wednesday, January 29nd

Room: 920 Burnside

Abstract:

I will describe a new notion of sectional curvature for 2-dimensional complexes. The 2-complexes with restricted sectional curvature have some remarkable properties:

Theorem: If X has nonpositive sectional curvature then every finitely generated subgroup of the fundamental group of X is finitely presented.

Theorem: If X has negative sectional curvature then:

1) Every finitely generated covering space of X has a compact core.

2) There are finitely many distinct conjugacy classes of indecomposable noncyclic subgroups of each rank in the fundamental group of X.

3) In many cases X is locally quasiconvex.

There are many beautiful examples with nonpositive and negative sectional curvature.