Steven Klee: Lower bounds for balanced simplicial polytopes and manifolds

A d-dimensional simplicial complex is called balanced if its graph admits a proper (d+1)-coloring.  Since the graph of a d-simplex is a complete graph on d+1 vertices, this represents the minimal coloring that such a complex could support.  

Many results on face enumeration for simplicial polytopes and simplicial manifolds have stronger balanced analogues that account for the extra structure imposed by the graph coloring.  In this talk, I will discuss connections to graph rigidity and the classical Lower Bound Theorem, the Generalized Lower Bound Theorem, and stellar moves on PL manifolds.