Weakly Bounded Cohomology Classes and a Counterexample to a Conjecture of Gromov

IF 2.4 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis Pub Date : 2024-02-14 DOI:10.1007/s00039-024-00676-9

引用次数: 0

Abstract

We exhibit a group of type F whose second cohomology contains a weakly bounded, but not bounded, class. As an application, we disprove a long-standing conjecture of Gromov about bounded primitives of differential forms on universal covers of closed manifolds.

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弱有界同调类和格罗莫夫猜想的一个反例

摘要我们展示了一个 F 型群，它的第二同调包含一个弱有界类，但不是有界类。作为一个应用，我们推翻了格罗莫夫关于闭流形普盖上微分形式有界基元的一个长期猜想。

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

Geometric and Functional Analysis 数学-数学

CiteScore

3.70

自引率

4.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Geometric And Functional Analysis (GAFA) publishes original research papers of the highest quality on a broad range of mathematical topics related to geometry and analysis. GAFA scored in Scopus as best journal in "Geometry and Topology" since 2014 and as best journal in "Analysis" since 2016. Publishes major results on topics in geometry and analysis. Features papers which make connections between relevant fields and their applications to other areas.