论文标题
Szczarba的扭曲Cochain是合理的
Szczarba's twisting cochain is comultiplicative
论文作者
论文摘要
我们证明了Szczarba的扭曲Cochain是合理的。特别是，从链条上的链条上的cobar构造X的cobar构造的诱导图是X的Kan Loop组上的链条上的链，这是DG双gebras的准同态。我们还表明，Szczarba的Twisted Shuffle Map是DGC地图，该地图将扭曲的笛卡尔产品与相关的扭曲张量产品连接起来。这为纤维束提供了天然的DGC模型。我们将结果应用于有限的覆盖空间和塞雷光谱序列。
We prove that Szczarba's twisting cochain is comultiplicative. In particular, the induced map from the cobar construction of the chains on a 1-reduced simplicial set X to the chains on the Kan loop group of X is a quasi-isomorphism of dg bialgebras. We also show that Szczarba's twisted shuffle map is a dgc map connecting a twisted Cartesian product with the associated twisted tensor product. This gives a natural dgc model for fibre bundles. We apply our results to finite covering spaces and to the Serre spectral sequence.
