We provide a random simplicial complex by applying standard constructions to a Poisson point process in Euclidean space. It is gigantic in the sense that - up to homotopy equivalence - it almost surely contains infinitely many copies of every compact topological manifold, both in isolation and in percolation.

中文翻译：

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巨大的随机单纯复形

我们通过将标准构造应用于欧几里得空间中的泊松点过程来提供随机单纯复形。从某种意义上说，它是巨大的——直到同伦等价——它几乎肯定包含每个紧凑拓扑流形的无限多个副本，无论是孤立的还是渗透的。