Montreal Geometric & Combinatorial Group Theory Seminar

Speaker: Dani
Wise (McGill)

Title: “Honeycombs
and tori in C(6) 2-complexes”

Date: 3:30pm
Wednesday, February 19th.

Room: 920
Burnside

Abstract:

The familiar
“honeycomb” hexagonal tessellation of the plane generalizes to the notion of a
“C(6) 2-complex” which has the property that a path traveling around a 2-cell
passes through at least 6 neighboring 2-cells.

Let *X* be a
compact C(6) complex. It is not hard to show that p_{1}*X* fails to be word-hyperbolic if and only if
*X *contains a honeycomb in its universal cover. Furthermore there is a
“periodic honeycomb” if and only if
Z´Z is a subgroup of p_{1}*X*.

The question is:
**Does the universal cover of X contain a honeycomb if and only if it contains
a periodic honeycomb?**

I suspect the answer is yes, and I will describe some partial results.