By a theorem of Banagl-Chriestenson, intersection spaces of depth one pseudomanifolds exhibit generalized Poincar\'{e} duality of Betti numbers, provided that certain characteristic classes of the link bundles vanish. In this paper, we show that the middle-perversity intersection space of a depth one Witt space can be completed to a rational Poincar\'{e} duality space by means of a single cell attachment, provided that a certain rational Hurewicz homomorphism associated to the link bundles is surjective. Our approach continues previous work of Klimczak covering the case of isolated singularities with simply connected links. For every singular stratum, we show that our condition on the rational Hurewicz homomorphism implies that the Banagl-Chriestenson characteristic classes of the link bundle vanish. Moreover, using Sullivan minimal models, we show that the converse implication holds at least in the case that twice the dimension of the singular stratum is bounded by the dimension of the link. As an application, we compare the signature of our rational Poincar\'{e} duality space to the Goresky-MacPherson intersection homology signature of the given Witt space. We discuss our results for a class of Witt spaces having circles as their singular strata.

中文翻译：

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深度一维特空间的交叉空间的基础类

根据 Banagl-Chriestenson 的定理，深度为一伪流形的交集空间表现出 Betti 数的广义 Poincar\'{e} 对偶性，前提是链接丛的某些特征类消失了。在本文中，我们证明了深度为 one Witt 空间的中间交叉空间可以通过单个单元格附着完成到有理 Poincar\'{e} 对偶空间，前提是某个有理 Hurewicz 同态与链接束是满射的。我们的方法延续了 Klimczak 之前的工作，涵盖了具有简单连接链接的孤立奇点的情况。对于每个奇异层，我们证明了我们在有理 Hurewicz 同态上的条件意味着链接丛的 Banagl-Chriestenson 特征类消失了。此外，使用 Sullivan 极小模型，我们表明，逆向蕴涵至少在奇异层维数的两倍受链接维数限制的情况下成立。作为一个应用，我们将有理 Poincar\'{e} 对偶空间的签名与给定 Witt 空间的 Goresky-MacPherson 交集同源签名进行比较。我们讨论了一类 Witt 空间的结果，这些空间将圆作为其奇异层。