We introduce a hyperbolic reflection group trick which builds closed aspherical manifolds out of compact ones and preserves hyperbolicity, residual finiteness, and—for almost all primes p—\(\mathbb{F} _{p}\)-homology growth above the middle dimension. We use this trick, embedding theory and manifold topology to construct Gromov hyperbolic 7-manifolds that do not virtually fiber over a circle out of graph products of large finite groups.

中文翻译：

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同源生长、双曲线化和纤维化

我们引入了一种双曲反射群技巧，它可以从紧致流形中构建闭合非球面流形，并保留双曲性、残差有限性，并且对于几乎所有素数p — \(\mathbb{F} _{p}\) - 中间以上的同调增长方面。我们使用这种技巧、嵌入理论和流形拓扑来构造格罗莫夫双曲 7 流形，该流形实际上不会在大型有限群的图积的圆上形成纤维。