The tangential Thom class of a Poincar茅 duality group

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• 作者：Yanghyun Byun ^{yhbyun@hanyang.ac.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：20J06 ; 57P10
• 刊名：Topology and its Applications
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：194
• 期：Complete
• 页码：349-357
• 全文大小：299 K

文摘

For each Poincaré duality group 螕 there exists a class, which we call the tangential Thom class of 螕, in the group cohomology of 螕×螕$\mathrm{螕}\times \mathrm{螕}$ with a right choice of the coefficient module. The class has the crucial properties, even if stated in a purely algebraic language, which correspond to those of Thom class of the tangent bundle of a closed manifold. In particular the Thom isomorphism has been proved to exist by observing that certain two sequences of homological functors, one being the homology of 螕 and the other that of 螕×螕$\mathrm{螕}\times \mathrm{螕}$, being regarded as functors defined on the category of Z螕$\mathbb{Z}\mathrm{螕}$-modules are homological and effaceable.