标题： 流形和群的虚拟纤维化 显示英文标题

标题： Virtual fibring of manifolds and groups

摘要： 本次调查的主题是流形上关于圆的纤维化现象，以及其群论上的对应概念，代数纤维化。 我们将讨论最新的研究状况，并简要解释一些近期发展的背后思想，重点关注RFRS群和具有此类基本群的流形。 然后我们将进入一个更具推测性的部分，在其中将提出关于高维纤维化的许多猜想。 这些猜想在可信度上各不相同，但即使是最大胆的猜想也可能与瑟斯顿关于“几乎纤维化猜想”的命运相似，瑟斯顿曾著名地说道： “这个听起来有些可疑的问题似乎有明确的可能性得到肯定的回答”。 显示英文摘要

摘要： The topic of this survey is the phenomenon of fibring over the circle for manifolds, and its group-theoretic twin, algebraic fibring. We will discuss the state of the art, and explain briefly some of the ideas behind the more recent developments, focusing on RFRS groups and manifolds with such fundamental groups. Then we will move on to a more speculative part, where many conjectures about fibring in higher dimensions will be given. The conjectures vary in their level of plausibility, but even the boldest of them might share the fate of Thurston's Virtually Fibred Conjecture, about which Thurston famously said: ``This dubious-sounding question seems to have a definite chance for a positive answer''.