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

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http://hdl.handle.net/10138/310769

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Pankka , P & Soultanis , E 2019 , ' Pull-Back of Metric Currents and Homological Boundedness of BLD-Elliptic Spaces ' , Analysis and Geometry in Metric Spaces , vol. 7 , no. 1 , pp. 212-249 . https://doi.org/10.1515/agms-2019-0011

Title: Pull-Back of Metric Currents and Homological Boundedness of BLD-Elliptic Spaces
Author: Pankka, Pekka; Soultanis, Elefterios
Contributor: University of Helsinki, Geometric Analysis and Partial Differential Equations
Date: 2019-03
Language: eng
Number of pages: 38
Belongs to series: Analysis and Geometry in Metric Spaces
ISSN: 2299-3274
URI: http://hdl.handle.net/10138/310769
Abstract: Using the duality of metric currents and polylipschitz forms, we show that a BLD-mappingf : X -> Y between oriented cohomology manifolds X and Y induces a pull-back operator f * : M-k,M-loc(Y) -> M-k,M-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,M-loc(X) -> M-k,M-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 R-n -> X.
Subject: Metric currents
BLD-mappings
QUASI-REGULAR MAPPINGS
BRANCHED COVERS
111 Mathematics
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