Pull-Back of Metric Currents and Homological Boundedness of BLD-Elliptic Spaces

Pekka Pankka 1  and Elefterios Soultanis 2
  • 1 University of Helsinki, , Helsinki, Finland
  • 2 SISSA, , University of Freiburg, , Trieste, Italy

Abstract

Using the duality of metric currents and polylipschitz forms, we show that a BLD-mapping f : XY 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 ℝnX.

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Analysis and Geometry in Metric Spaces (AGMS) is a fully peer-reviewed, open access electronic journal that publishes cutting-edge original research on analytical and geometrical problems in metric spaces and their mathematical applications. It features articles making connections among relevant topics in this field.

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