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



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 p1X 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 p1X.


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.