论文标题
有限的统治和Novikov同源性强烈$ \ mathbb {z}^2 $ raded环
Finite domination and Novikov homology over strongly $\mathbb{Z}^2$-graded rings
论文作者
论文摘要
令$ r $为强烈的$ \ mathbb {z}^2 $分级环，让$ c $为有限生成的免费$ r $ modules的有限链链。复杂的$ c $是$ r _ {（0,0）} $ - 有限主导，或$ r _ {（0,0）} $的FP类型，如果它是链均值等同于有限生成的投影型$ r _ {（0,0,0）} $ - 模块的有限生成的投影型复合物。我们表明，这种情况只有$ c $在带有一定八个正式电源系列的张量产品之后才变成无环，这就是古典诺维科夫戒指的分级类似物。这扩展了Ranicki，Quinn和第一和两个不确定的Laurent多项式环的第一作者。
Let $R$ be a strongly $\mathbb{Z}^2$-graded ring, and let $C$ be a bounded chain complex of finitely generated free $R$-modules. The complex $C$ is $R_{(0,0)}$-finitely dominated, or of type FP over $R_{(0,0)}$, if it is chain homotopy equivalent to a bounded complex of finitely generated projective $R_{(0,0)}$-modules. We show that this happens if and only if $C$ becomes acyclic after taking tensor product with a certain eight rings of formal power series, the graded analogues of classical Novikov rings. This extends results of Ranicki, Quinn and the first author on Laurent polynomial rings in one and two indeterminates.
