论文标题
在简单络合物上的等效性神经引理，简单差异和配置空间的模型
Equivariant Nerve Lemma, simplicial difference, and models for configuration spaces on simplicial complexes
论文作者
论文摘要
威尔特郡 - 戈登（Wiltshire-Gordon）已在给定的简单复合物上引入了一个用于有序配置空间的同质模型。该作者断言，在合适的细分之后，他的模型也适用于无序的配置空间。我们提供了详细信息，证明了威尔特郡 - 戈登的断言是合理的，更重要的是，揭示了他更普通的简单差异模型的模棱两可的属性，以补充一个较大的复合体内部的子复杂性。这是通过证明神经引理的模棱两可的版本来实现的。另外，在配置空间的情况下，我们表明该模型的略有变化具有更好的属性：它是常规的，并且在配置空间内部是强大而模棱两可的变形缩回。我们对配置空间模型的变体来自威尔特郡的简单差异与众所周知的模型之间的比较。
Wiltshire-Gordon has introduced a homotopy model for ordered configuration spaces on a given simplicial complex. That author asserts that, after a suitable subdivision, his model also works for unordered configuration spaces. We supply details justifying Wiltshire-Gordon's assertion and, more importantly, uncover the equivariant properties of his more-general simplicial-difference model for the complement of a subcomplex inside a larger complex. This is achieved by proving an equivariant version of the Nerve Lemma. In addition, in the case of configuration spaces, we show that a slight variation of the model has better properties: it is regular and sits inside the configuration space as a strong and equivariant deformation retract. Our variant for the configuration-space model comes from a comparison, in the equivariant setting, between Wiltshire's simplicial difference and a well known model for the complement of a full subcomplex on a simplicial complex.
