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- W2950120006 abstract "Kalai proved that the simplicial polytopes with g_2=0 are the stacked polytopes. We characterize the g_2=1 case. Specifically, we prove that every simplicial d-polytope (d>=4) which is prime and with g_2=1 is combinatorially equivalent either to a free sum of two simplices whose dimensions add up to d (each of dimension at least 2), or to a free sum of a polygon with a (d-2)-simplex. Thus, every simplicial d-polytope (d>=4) with g_2=1 is combinatorially equivalent to a polytope obtained by stacking over a polytope as above. Moreover, the above characterization holds for any homology (d-1)-sphere (d>=4) with g_2=1, and our proof takes advantage of working with this larger class of complexes." @default.
- W2950120006 created "2019-06-27" @default.
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- W2950120006 date "2008-04-10" @default.
- W2950120006 modified "2023-09-27" @default.
- W2950120006 title "A characterization of simplicial polytopes with g_2 = 1" @default.
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