投影的Leray数与拓扑Helly型定理
Leray numbers of projections and a topological Helly type theorem
摘要：
设X是顶点集V上的单纯复形，X的有理Leray数L（X）是使得X的任意诱导子复形的有理约化同调在维数d及以上为零的最小d.设π是从X到单形Y的单形映射，使得|Y|中任一点的原像的基数至多为r.证明了L（π（X））\leq rL（X）+r-1.一个后果是一个拓扑扩展的Helly型结果Amenta。
英文摘要：
Let X be a simplicial complex on the vertex set V. The rational Leray number L(X) of X is the minimal d such that the rational reduced homology of any induced subcomplex of X vanishes in dimensions d and above. Let πbe a simplicial map from X to a simplex Y, such that the cardinality of the preimage of any point in |Y| is at most r. It is shown that L(π(X)) \leq r L(X)+r-1. One consequence is a topological extension of a Helly type result of Amenta.
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