BLD-椭圆空间度量流的拉回与同调有界性
Pull-back of metric currents and homological boundedness of BLD-elliptic spaces
摘要：
利用度量流和polylipschitz形式的对偶性，证明了定向上同调流形$X$和$Y$之间的BLD-映射$f\colon X\to Y$在局部有限质量的度量流$k$ -流空间之间诱导出一个拉回算子$f^\ast \colon M_{k,loc}(Y) \to M_{k,loc}(X)$.对于适当的映射，拉回是前推$f_\ast \colon M_{k,loc}(X)\to M_{k,loc}(Y)$的右逆（直到重数）。作为应用，我们得到了Bonk和Heinonen的上同调有界性定理在局部Lipschitz可缩上同调$n$ -流形$X$中的一个非光滑形式，其中$X$允许一个BLD-映射$\mathbb{R}^n \to X$ .
英文摘要：
Using the duality of metric currents and polylipschitz forms, we show that a BLD-mapping $f\colon X\to Y$ between oriented cohomology manifolds $X$ and $Y$ induces a pull-back operator $f^\ast \colon M_{k,loc}(Y) \to M_{k,loc}(X)$ 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 $f_\ast \colon M_{k,loc}(X)\to M_{k,loc}(Y)$. 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 $\mathbb{R}^n \to X$.
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