====== Andy Fromader (Cornell) ======

====== The Charney-Davis Conjecture for Certain Spheres ======

===== Abstract for the Combinatorics and Geometry/Topology Seminars 2009 March 17 =====

The Charney-Davis conjecture is an easily stated linear inequality on the face numbers of simplicial spheres that are also flag complexes, that is, complexes for which every minimal non-face is a two element set. While the conjecture is reasonably well known, it is only known to hold in a handful of rather narrow cases, and the proofs are often very complicated. I will discuss some known results and give an easy proof of a relatively broad case.


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