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.

中文翻译：

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弱有界上同调类和格罗莫夫猜想的反例

摘要

我们展示了一个 F 型群，其第二上同调包含一个弱有界但无界的类。作为一个应用，我们反驳了格罗莫夫关于闭流形通用覆盖上微分形式有界本元的长期猜想。