论文标题
有界的无环和相对简单量
Bounded acyclicity and relative simplicial volume
论文作者
论文摘要
我们为相对简单体积提供了新的消失和胶合效果，跟随有界的同一个共同体中的两个当前主题：从木制组到有限的无环组和使用模棱两可的拓扑。 更确切地说，我们考虑了亚组家族家庭的模棱两可的神经对和相对分类空间。通常，我们将其应用于亚组的统一无环族。我们的方法还导致$ \ ell^2 $ -betti数量的非球体CW对消失的结果，其相对amenable类别是小的，以及Dranishnikov和Rudyak的结果的相对版本，涉及映射程度和基本组的遗传。
We provide new vanishing and glueing results for relative simplicial volume, following up on two current themes in bounded cohomology: The passage from amenable groups to boundedly acyclic groups and the use of equivariant topology. More precisely, we consider equivariant nerve pairs and relative classifying spaces for families of subgroups. Typically, we apply this to uniformly boundedly acyclic families of subgroups. Our methods also lead to vanishing results for $\ell^2$-Betti numbers of aspherical CW-pairs with small relative amenable category and to a relative version of a result by Dranishnikov and Rudyak concerning mapping degrees and the inheritance of freeness of fundamental groups.
