{"paper":{"title":"Pull-back of metric currents and homological boundedness of BLD-elliptic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.MG","authors_text":"Elefterios Soultanis, Pekka Pankka","submitted_at":"2018-09-09T17:22:08Z","abstract_excerpt":"Using the duality of metric currents and polylipschitz forms, we show that a BLD-mapping $f\\colon X\\to Y$ between oriented cohomology manifolds $X$ and $Y$ induces a pull-back operator $f^\\ast \\colon M_{k,loc}(Y) \\to M_{k,loc}(X)$ 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 $f_\\ast \\colon M_{k,loc}(X)\\to M_{k,loc}(Y)$. As an application we obtain a non-smooth version of the cohomological boundedness theorem of Bonk and Heinonen for locally Lipschitz contractible cohomology $n$-manif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03009","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}