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- W1488605148 abstract "In this paper we prove that a simplicial map of finite-dimensional locally finite simplicial complexes has contractible point inverses if and only if it is an $epsilon$-controlled homotopy equivalence for all $epsilon>0$ if and only if $ftimes mathrm{id}_mathbb{R}$ is a bounded homotopy equivalence measured in the open cone over the target. This confirms for such a space $X$ the slogan that arbitrarily fine control over $X$ corresponds to bounded control over the open cone $O(X_+)$. For the proof a one parameter family of cellulations ${X_epsilon^prime}_{0<epsilon<epsilon(X)}$ is constructed which provides a retracting map for $X$ which can be used to compensate for sufficiently small control." @default.
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- W1488605148 date "2013-10-11" @default.
- W1488605148 modified "2023-09-27" @default.
- W1488605148 title "A controlled local-global theorem for simplicial complexes" @default.
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