Abstract Using the duality of metric currents and polylipschitz forms, we show that a BLD-mapping f : X → Y between oriented cohomology manifolds X and Y induces a pull-back operator f* : Mk,loc(Y) → Mk,loc(X) between the spaces of metric k-currents of locally finite mass. For proper maps, the pull-back is a right-inverse (up to multiplicity) of the push-forward f* : Mk,loc(X) → Mk,loc(Y). As an application we obtain a non-smooth version of the cohomological boundedness theorem of Bonk and Heinonen for locally Lipschitz contractible cohomology n-manifolds X admitting a BLD-mapping ℝn → X.

中文翻译：

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BLD-椭圆空间的度量电流的回拉和同调有界

摘要 使用度量电流和 polylipschitz 形式的对偶性，我们证明了定向上同调流形 X 和 Y 之间的 BLD 映射 f : X → Y 诱导了回拉算子 f* : Mk,loc(Y) → Mk,loc( X) 在局部有限质量的度量 k 电流空间之间。对于正确的映射，回拉是前推 f* 的右逆（最多多重）：Mk,loc(X) → Mk,loc(Y)。作为一个应用，我们获得了 Bonk 和 Heinonen 的上同调有界定理的非光滑版本，用于局部 Lipschitz 可收缩上同调 n 流形 X 允许 BLD 映射 ℝn → X。