AI 中文总结
本文构造了亏格二双曲曲面乘积的有限覆盖，其基本群生成元数有界而内射半径趋于无穷，为高秩对称空间上的 Avramidi-Delzant 猜想提供了反例。
AI 中文摘要
我们构造了一个固定的两个亏格为二的闭双曲曲面乘积的有限覆盖，其基本群由至多十五个元素生成，且其内射半径趋于无穷。该构造使用有限群上的纤维积。这些覆盖是闭的 aspherical 四维流形，其万有覆盖为 $\mathbb H^2\times\mathbb H^2$。它们为 Avramidi 和 Delzant 关于高秩对称空间的猜想在 $\mathbb H^2\times\mathbb H^2$ 情形下提供了反例。
英文摘要
We construct finite covers of a fixed product of two closed hyperbolic surfaces of genus two whose fundamental groups are generated by at most fifteen elements and whose injectivity radii tend to infinity. The construction uses fibre products over finite groups. These covers are closed aspherical four-manifolds with universal cover $\mathbb H^2\times\mathbb H^2$. They give counterexamples to a conjecture of Avramidi and Delzant for symmetric spaces of higher rank, in the case \(\mathbb H^2\times\mathbb H^2\).
