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

Thursday, November 13, 2014 - 2:00pm - 2:50pm
Keller 3-180
Isabella Novik (University of Washington)
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.
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