Balanced manifolds and pseudomanifolds

Abstract

A simplicial (d − 1)-dimensional complex K is called balanced if the graph of K (i. e., the, the 1-dimensional skeleton) is d-colorable. Here we discuss some recent results as well as several open questions on face numbers of balanced manifolds and pseudomanifolds; we also present constructions of balanced manifolds (with and without boundary) with few vertices. This work is joint with Steve Klee.