论文标题
关于有限统治和庞加莱二元性
On Finite domination and Poincaré duality
论文作者
论文摘要
本文的目的是表明非同性恋有限的庞加莱二元空间很多。令$π$有限地呈现。假设减少的Grothendieck组$ \ tilde k_0（\ bbb z [π]）$具有非平凡的2个元素，我们构建了一个有限支配的Poincaréspace $ x $，带有基本组$π$，因此$ x $不是同质的。 $ x $的尺寸可以任意大。我们的证明依赖于结果，该结果表明，每个有限统治的空间都具有稳定的庞加尔二重性增厚。
The object of this paper is to show that non-homotopy finite Poincaré duality spaces are plentiful. Let $π$ be finitely presented group. Assuming that the reduced Grothendieck group $\tilde K_0(\Bbb Z[π])$ has a non-trivial 2-divisible element, we construct a finitely dominated Poincaré space $X$ with fundamental group $π$ such that $X$ is not homotopy finite. The dimension of $X$ can be made arbitrarily large. Our proof relies on a result which says that every finitely dominated space possesses a stable Poincaré duality thickening.
