AI 中文总结
研究随机流形欧拉特征，证明了随机水平曲面H的欧拉特征期望公式，还表明子流形的f - 向量期望与宿主流形的f - 向量明确相关。
AI 中文摘要
我们证明了在给定单纯复形G中随机水平曲面H的欧拉特征X(H)的期望为E[X(H)] =2 - 2K(G) - X(G)，其中K(G)=1 - f_0/2 + f_1/3 -...是G的曲率泛函，X(G)=f_0 - f_1 + f_2 -...是欧拉特征。更一般地，子流形的f - 向量期望与宿主流形的f - 向量明确相关。
英文摘要
We prove that the expectation of the Euler characteristic X(H) of random level surface H in a given simplicial complex G is E[X(H)] =2-2K(G)-X(G), where K(G)=1-f_0/2+f_1/3- ... is the curvature functional of G and X(G)=f_0-f_1+f_2-... is the Euler characteristics. More generally, the expectation of the f-vector of a submanifold is explicitly linked to the f-vector of the host manifold.
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