关于极小非面少的同调球面
On homology spheres with few minimal non faces
摘要：
设Δ是n个顶点上的（d-1）维同调球面，具有m个极小非面.考虑不变量α：= m -（n-d），证明了对于给定的α值，只有1/2个同调球面不能通过一点悬挂和另一点悬挂得到.此外，我们描述了所有α不超过4的同调球，作为推论，所有最小非面不超过8的同调球。为了证明这些结果，我们考虑Δ的最小非面的神经。
英文摘要：
Let Δbe a (d-1)-dimensional homology sphere on n vertices with m minimal non-faces. We consider the invariant α:= m - (n-d) and prove that for a given value of α, there are only finitely many homology spheres that cannot be obtained through one-point suspension and suspension from another. Moreover, we describe all homology spheres with αup to four and, as a corollary, all homology spheres with up to eight minimal non-faces. To prove these results we consider the nerve of the minimal non-faces of Δ.
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