标题： 四元数群的奇异表示和沃伦的D2问题 显示英文标题

标题： Exotic presentations of quaternion groups and Wall's D2 problem

摘要： D2问题由C. T. C. Wall提出，询问是否每个有限共调2维的CW复形都同伦等价于一个有限2复形。已经提出了几个潜在的反例，其中最持久的是由Cohen和Dyer构造的一个CW复形，其基本群是阶为32的四元数群。我们证明这个CW复形同伦等价于Mannan-Popiel构造的一个表示2复形，从而表明它不是D2问题的反例。接下来，我们引入一个阶为$4n$的四元数群的无限个表示族，并证明它们实现了Mannan-Popiel的表示所无法实现的同伦类型。 显示英文摘要

摘要： The D2 problem of C. T. C. Wall asks whether every finite cohomologically 2-dimensional CW-complex is homotopy equivalent to a finite 2-complex. Several potential counterexamples have been proposed, the longest standing of which is a CW-complex constructed by Cohen and Dyer whose fundamental group is a quaternion group of order 32. We show that this CW-complex is homotopy equivalent to the presentation 2-complex of a presentation constructed by Mannan-Popiel, thus showing it is not a counterexample to the D2 problem. We next introduce an infinite family of presentations for a quaternion group of order $4n$ and prove that they achieve homotopy types which are not achieved by the presentations of Mannan-Popiel.