A 𝑄-manifold local-compactification of a metric combinatorial ∞-manifold

Sakai, Katsuro

doi:10.1090/S0002-9939-1987-0894453-6

A $Q$-manifold local-compactification of a metric combinatorial $\infty$-manifold
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Proc. Amer. Math. Soc. 100 (1987), 775-780 Request permission

Abstract:

Let $K$ be a combinatorial $\infty$-manifold, that is, a countable simplicial complex such that the star of each vertex is combinatorially equivalent to the countable-infinite full simplicial complex. Then the space ${\left | K \right |_m}$ with the metric topology is a manifold modeled on the space $\sigma$, where $\sigma$ is the subspace of the Hilbert cube $Q = {I^\omega }$ which consists of all points having at most finitely many nonzero coordinates. In this paper, we give a local-compactification of ${\left | K \right |_m}$ which is a $[0,1)$-stable $Q$-manifold containing ${\left | K \right |_m}$ as an f.d. cap set.

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