Suppose [Formula: see text] is a discrete group, and [Formula: see text], with [Formula: see text] an abelian group. Given a representation [Formula: see text], with [Formula: see text] a closed 3-manifold, put [Formula: see text], where [Formula: see text] is a continuous map inducing [Formula: see text] which is unique up to homotopy, and [Formula: see text] is the pairing. We extend the definition of [Formula: see text] to manifolds with corners, and establish a gluing law. Based on these, we present a practical method for computing [Formula: see text] when [Formula: see text] is given by a surgery along a link [Formula: see text]. In particular, the Chern–Simons invariant can be computed this way.

中文翻译：

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3-流形群表示的上同调不变量

假设 [Formula: see text] 是一个离散群，而 [Formula: see text] 与 [Formula: see text] 是一个阿贝尔群。给定一个表示 [Formula: see text]，其中 [Formula: see text] 是一个封闭的 3-manifold，放置 [Formula: see text]，其中 [Formula: see text] 是一个连续映射，导致 [Formula: see text]在同伦上是唯一的，[公式：见正文]是配对。我们将[公式：见正文]的定义扩展到有角的流形，并建立了粘合定律。基于这些，我们提出了一种计算[公式：见文本]的实用方法，当[公式：见文本]通过链接[公式：见文本]通过手术给出时。特别是，可以通过这种方式计算 Chern-Simons 不变量。