论文标题
取消$（g，n）$ - 复合物和天鹅的有限障碍物
Cancellation for $(G,n)$-complexes and the Swan finiteness obstruction
论文作者
论文摘要
在以前的工作中，我们将有限$（g，n）$的同件类型相关联时，当$ g $具有定期的共同体学$ \ mathbb {z} g $ - 模块，代表了天鹅的有限障碍。我们用它来确定$ x \ vee s^n \ simeq y \ vee s^n $意味着有限$（g，n）$ - 复合物$ x $ $ x $和$ y $的$ x \ simeq y $，并在失败时给出同型不同对的较低界限。证明涉及构建投影$ \ mathbb {z} g $模块作为本地免费模块的升降机，而不是Quaternion代数产品的订单，其存在的存在于Eichler Mass Formula。在$ n = 2 $的情况下，出现了困难，这导致了一种新的方法来找到沃尔的D2问题的反例。
In previous work, we related homotopy types of finite $(G,n)$-complexes when $G$ has periodic cohomology to projective $\mathbb{Z} G$-modules representing the Swan finiteness obstruction. We use this to determine when $X \vee S^n \simeq Y \vee S^n$ implies $X \simeq Y$ for finite $(G,n)$-complexes $X$ and $Y$, and give lower bounds on the number of homotopically distinct pairs when this fails. The proof involves constructing projective $\mathbb{Z} G$-modules as lifts of locally free modules over orders in products of quaternion algebras, whose existence follows from the Eichler mass formula. In the case $n=2$, difficulties arise which lead to a new approach to finding a counterexample to Wall's D2 problem.
