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

IF 0.9 3区数学 Q2 MATHEMATICS

Analysis and Geometry in Metric Spaces Pub Date : 2018-09-09 DOI:10.1515/agms-2019-0011

Pekka Pankka, Elefterios Soultanis

引用次数: 2

Abstract

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). 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 ℝn → X.

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度量电流的回拉与bld -椭圆空间的同调有界性

摘要利用度量电流和polyipschitz形式的对偶性，我们证明了一个BLD映射f:X→ Y在有向上同调流形X和Y之间诱导拉回算子f*：Mk，loc（Y）→ Mk，loc（X）在局部有限质量的度量k-流的空间之间。对于适当的映射，拉回是向前推进f*的右逆（高达多重）：Mk，loc（X）→ Mk，loc（Y）。作为一个应用，我们得到了局部Lipschitz可压缩上同调n-流形X的Bonk和Heinonen上同调有界性定理的一个非光滑版本，该定理允许BLD映射ℝn→ 十、

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.