Talk page
Title:
Sphere triangulations, Dual Graphs, and Expanders
Speaker:
Abstract:
Kalai asked whether the dual graphs of a family of simplicial 4-polytopes can be an expander family; Gromov asked the analogous question for the dual graphs of simplicial 3-spheres. A construction due to Loiskekoski and Ziegler shows that there exists a family of simplicial 4-polytopes whose dual graphs do not have small separators, but their examples do not form an expander family. We construct a family of (possibly non-polytopal) simplicial 3-spheres whose dual graphs do expand. More generally, we describe a flexible method to construct simplicial homology spheres from a certain class of bounded-degree graphs. Based on joint work with Karim Adiprasito.
Link:
Workshop: