论文标题
Borel-Moore同源性的伪细胞
Pseudocycles for Borel-Moore Homology
论文作者
论文摘要
伪细胞是平滑流形的整体同源类类别的几何代表，事实证明，这对于定义量规理论不变性特别有用。与通常的同源性相比，在非紧密歧管的情况下，Borel-Moore同源性通常是一个更自然的对象。我们定义了伪细胞和伪细胞等效性的标准概念的较弱版本，然后描述这些较弱的伪循环和Borel-Moore同源性的等效类别之间的天然同构。我们还包括一个直接证明，在定向歧管的奇异共同体及其Borel-Moore同源性之间具有庞加莱双重性。
Pseudocycles are geometric representatives for integral homology classes on smooth manifolds that have proved useful in particular for defining gauge-theoretic invariants. The Borel-Moore homology is often a more natural object to work with in the case of non-compact manifolds than the usual homology. We define weaker versions of the standard notions of pseudocycle and pseudocycle equivalence and then describe a natural isomorphism between the set of equivalence classes of these weaker pseudocycles and the Borel-Moore homology. We also include a direct proof of a Poincaré Duality between the singular cohomology of an oriented manifold and its Borel-Moore homology.
