BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Graded Betti numbers of balanced simplicial complexes Juhnke-Kubitzke, Martina


A $(d-1)$-dimensional simplicial complex is called balanced, if its $1$-skeleton is $d$-colorable. In this talk, I will discuss upper bounds for the graded Betti numbers of the Stanley-Reisner rings of this class of simplicial complexes. Our results include both, bounds for the Cohen-Macaulay case and for the general situation. Previously, upper bounds have been shown by Migliore and Nagel, and Murai for simplicial polytopes, Cohen-Macaulay complexes and normal pseudomanifolds. If time permits, I will also mention, what can be said for balanced normal pseudomanifolds. This is joint work with Lorenzo Venturello.

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