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.