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

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).

Keywords

• metric currents
• bld-mappings
• 30l10
• 49q15
• 30c65