Cube Complexes and their Growth Series

Richard Scott
Santa Clara University
Professor

“A cube complex Y is a geometric object constructed by gluing together Euclidean cubes along their faces. If G is the fundamental group of Y, then there is an induced length function ℓ:G→Z≥0 defined by letting ℓ(g) be the number of edges in a minimal edge-path representing the loop g ∈ G. The corresponding growth series of G, is then defined to be the power series G(q) = Σg∈G q^ℓ(g).
In this talk, we will show how certain combinatorial conditions on the cube  complex can impose surprising algebraic properties of G(q)”.

View Scott’s Event Flyer