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BY 4.0 license Open Access Published by De Gruyter Open Access November 25, 2019

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

  • Pekka Pankka and Elefterios Soultanis EMAIL logo


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.

MSC 2010: 30L10; 49Q15; 30C65


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Received: 2019-06-10
Accepted: 2019-10-15
Published Online: 2019-11-25

© 2019 Pekka Pankka et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 Public License.

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