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Lower Bound Theorems and a Generalized Lower Bound Conjecture for Balanced Simplicial Complexes

Presenter
November 13, 2014
Keywords:
  • Dimensional analysis
MSC:
  • 00A73
Abstract
A simplicial (d-1)-dimensional complex K is called "balanced" if the graph of K is d-colorable. Rather surprisingly, it turns out that many well-known face enumeration results have natural balanced analogs (or at least conjectural analogs). Specifically, we will discuss the balanced analog of the celebrated Lower Bound Theorem (together with the treatment of equality cases) and the balanced analog of the Generalized Lower Bound Conjecture. If there is time, we will also talk about the balanced Walkup class and present constructions of balanced manifolds with few vertices. This work is joint with Steve Klee.