广义图流形、剩余有限性与Singer猜想
Generalized Graph Manifolds, Residual Finiteness, and the Singer Conjecture
AI总结：
本文证明了扩展图流形和纯复双曲高维图流形在基本群剩余有限条件下的Singer猜想，并用Price型不等式重新证明三维情形的Lott–Lueck结果，同时构造了多类基本群剩余有限的高维图流形。
摘要：
我们证明了扩展图流形以及具有剩余有限基本群的纯复双曲高维图流形的Singer猜想。在实三维情形中，Hempel的一个结果保证了基本群总是剩余有限的，我们随后给出了Lott和Lueck一个著名结果的Price型不等式证明。最后，我们给出了若干类确实具有剩余有限基本群的高维图流形。
英文摘要：
We prove the Singer conjecture for extended graph manifolds and pure complex-hyperbolic higher graph manifolds with residually finite fundamental groups. In real dimension three, where a result of Hempel ensures that the fundamental group is always residually finite, we then provide a Price type inequality proof of a well-known result of Lott and Lueck. Finally, we give several classes of higher graph manifolds which do indeed have residually finite fundamental groups.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
