论文标题
复合体类别的链二元性
Chain duality for categories over complexes
论文作者
论文摘要
我们表明，由有限的简单复合物$ k $参数为链二元性的链条复合物的添加剂类别。这一事实从未在最初的参考文献中得到充分证明，这对于拉尼基（Ranicki）对手术的代数制定了Sullivan和Wall的精确序列，以及他对手术阻塞图的解释是从当地Poincaré二元性到全球庞加莱二元性的通道。我们的论文还提供了基于$ k $的连锁综合体的链二重性的新，概念和几何处理。
We show that the additive category of chain complexes parametrized by a finite simplicial complex $K$ forms a category with chain duality. This fact, never fully proven in the original reference, is fundamental for Ranicki's algebraic formulation of the surgery exact sequence of Sullivan and Wall, and his interpretation of the surgery obstruction map as the passage from local Poincaré duality to global Poincaré duality. Our paper also gives a new, conceptual, and geometric treatment of chain duality on $K$-based chain complexes.
