对应于三维单纯球面的矩角流形、弦性与球面乘积连通和
Moment-angle manifolds corresponding to three-dimensional simplicial spheres, chordality and connected sums of products of spheres
AI总结：
本文刻画了三维单纯球面K的矩角复形上同调环同构于球面乘积连通和的条件，并推广到任意维单纯球面的充分条件。
摘要：
我们证明，对应于三维单纯球面$K$的矩角复形$\mathcal Z_K$的上同调环同构于球面乘积连通和的上同调环当且仅当以下条件之一成立：(a) $K$是四维交叉多面体的边界，(b) $K$的一维骨架是弦图，或(c) $K$中恰好有两个缺失边且它们构成一个无弦4-圈。对于任意维数的单纯球面$K$，我们得到了环同构$H^*(\mathcal Z_K)\cong H^*(M)$的一个充分条件，其中$M$是球面乘积的连通和。
英文摘要：
We prove that the moment-angle complex $\mathcal Z_K$ corresponding to a 3-dimensional simplicial sphere $K$ has the cohomology ring isomorphic to the cohomology ring of a connected sum of products of spheres if and only if either (a) $K$ is the boundary of a 4-dimensional cross-polytope, or (b) the one-skeleton of $K$ is a chordal graph, or (c) there are only two missing edges in $K$ and they form a chordless 4-cycle. For simplicial spheres $K$ of arbitrary dimension, we obtain a sufficient condition for the ring isomorphism $H^*(\mathcal Z_K)\cong H^*(M)$ where $M$ is a connected sum of products of spheres.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
