PD₄-complexes with fundamental group a PD₂-group

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• 作者：Hillman ; Jonathan A.
• 关键词：57P10 ; 4-manifold ; Poincaré ; duality ; Surface group
• 刊名：Topology and its Applications
• 出版年：2004
• 期刊代码：60_01668641
• 类别：mt
• 出版时间：July 28, 2004
• 卷：142
• 期：1-3
• 页码：49-60
• 文件大小：253 K

摘要

We show that if the fundamental group π of a PD₄-complex X has cohomological dimension 2 there is a 2-connected degree 1 map from X to a “minimal” such complex. If moreover π has one end we relate the cohomological linking pairing to the attaching map for the top cell via the Whitehead quadratic functor, and show that every w-hermitian form on a finitely generated projective Z[π]-module is realized by some PD₄-complex with fundamental group π. If π is a PD₂-group the minimal complex is the total space of an Sp>2p>-bundle over K(π,1) and is determined by cohomological invariants of X.