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- W2892235170 abstract "We define the space $Gamma_c^k(X)$ of polylipschitz $k$-forms on a metric space $X$ and show that it yields a pre-dual for the space of metric $k$-currents $mathscr D_k(X)$ of Ambrosio and Kirchheim. Using polylipschitz forms, we show that a BLD-mapping $f:Xto Y$ between oriented cohomology manifolds $X$ and $Y$ induces a pull-back operator $f^*:M_{k,loc}(Y)to M_{k,loc}(X)$ 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 $f_*:M_{k,loc}(X)to M_{k,loc}(Y )$. 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 $mathbb R^nto X$." @default.
- W2892235170 created "2018-09-27" @default.
- W2892235170 creator A5024411845 @default.
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- W2892235170 date "2018-09-09" @default.
- W2892235170 modified "2023-09-27" @default.
- W2892235170 title "Metric currents, polylipschitz forms and homological boundedness of BLD-elliptic spaces." @default.
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