Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, May 22, 2008, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Eran Nevo (Cornell Univ., Ithaca)

A characterization of simplicial polytopes with g₂=1

Let $v$ and $e$ be the numbers of vertices and edges, respectively, of a simplicial polytope $P$. Define $g_2(P)=e-dv+\binom{d+1}{2}$. Barnette proved that $g_2(P)$ is nonnegative. Kalai proved that the simplicial polytopes with $\g_2=0$ are the stacked polytopes ($d\geq 4$). We characterize the $\g_2=1$ case. It turns out they are the polytopes obtained by stacking over either a join of two simplices, each of dimension at least two, whose dimensions add up to $d$, or a join of a polygon with a $(d-2)$-simplex ($d\geq 4$). The proof uses rigidity theory of graphs and Alexander duality, and works in the generality of homology spheres. Related problems will be mentioned. All the needed notions will be explained in the talk.

Joint work with Eyal Novinsky.

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