论有限支配和泊恩卡对偶性

IF 0.8 4区数学 Q2 MATHEMATICS

Homology Homotopy and Applications Pub Date : 2024-01-24 DOI:10.4310/hha.2024.v26.n1.a3

John R. Klein

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引用次数: 0

摘要

本文的目的是证明非同向有限波恩卡列对偶空间是非常多的。假设 $π$ 是一个有限呈现群。假定还原的格罗内狄克群 $\widetilde{K}_0 (\mathbb{Z} [\pi])$ 有一个非三价的 2 美元可分元素，我们将构造一个有限支配的、基群为 $π$ 的波恩卡列空间 $X$，使得 $X$ 不是同调有限的。$X$ 的维数可以任意变大。我们的证明依赖于一个结果，即每个有限支配空间都拥有一个稳定的波恩卡列对偶增厚。

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On finite domination and Poincaré duality

The object of this paper is to show that non-homotopy finite Poincaré duality spaces are plentiful. Let $π$ be a finitely presented group. Assuming that the reduced Grothendieck group $\widetilde{K}_0 (\mathbb{Z} [\pi])$ 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.

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来源期刊

Homology Homotopy and Applications 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.