Real Root Conjecture fails for five and higher dimensional spheres

Abstract

A construction of convex flag triangulations of five and higher dimensional spheres, whose h-polynomials fail to have only real roots, is given. We show that there is no such example in dimensions lower than five. A condition weaker than realrootedness is conjectured and some evidence is provided

15 pages, 1 figure

References in corpus (2)

• Weighted $L^2$-cohomology of Coxeter groups
• The cd-index of fans and lattices

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