Bredon-Poincare对偶群
Bredon-Poincare Duality Groups
摘要：
若$G$是一个允许$\mathrm{B}G$有流形模型的群，则$G$是一个Poincaré对偶群.我们研究了推广的庞加莱对偶群，最初介绍了戴维斯和Leary，动机组$G$与共紧流形模型$M$为$\underline{\mathrm{E}}G$其中$M^H$是一个可收缩子流形的所有有限子群$H$的$G$。我们给出了这些Bredon-Poincaré对偶群的例子和构造的几个来源，包括使用Davis和Leary的等变反射群技巧来构造Bredon-Poincaré对偶群的例子，这些对偶群是由流形$M$上的作用产生的，其中指定了子流形$M^H$的维数。我们对低维的Bredon-Poincaré对偶群进行了分类，并讨论了在群扩张和群图下的行为。
英文摘要：
If $G$ is a group which admits a manifold model for $\mathrm{B}G$ then $G$ is a Poincaré duality group. We study a generalisation of Poincaré duality groups, introduced initially by Davis and Leary, motivated by groups $G$ with cocompact manifold models $M$ for $\underline{\mathrm{E}}G$ where $M^H$ is a contractible submanifold for all finite subgroups $H$ of $G$. We give several sources of examples and constructions of these Bredon-Poincaré duality groups, including using the equivariant reflection group trick of Davis and Leary to construct examples of Bredon-Poincaré duality groups arising from actions on manifolds $M$ where the dimensions of the submanifolds $M^H$ are specified. We classify Bredon-Poincaré duality groups in low dimensions, and discuss behaviour under group extensions and graphs of groups.
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