论文标题
分组模块的侵犯图
Transgression maps for crossed modules of groupoids
论文作者
论文摘要
给定一个crossed classoids $ n \ rightarrow g $，我们构造了（1）来自产品groupoid $ \ mathbb {z} \ times（n \ rtimes g）\ rightrightArrows n $的天然同态$ h^\ ast（g_ \ bullet，\ mathbb {z}）$ g $ g $的神经$ g $的$ h^{\ ast-ast-1} \ big（（（n \ rtimes g）_ \ bult，\ mathbb {z} \ mathb {z} \ big）的$ nvere $ ncross $ n cross $ g n cross $ ncross $ ncross。事实证明，后者与Tu-Xu在其对高度$ k $ - 理论的研究中获得的违法图相同。
Given a crossed module of groupoids $N\rightarrow G$, we construct (1) a natural homomorphism from the product groupoid $\mathbb{Z}\times(N\rtimes G)\rightrightarrows N$ to the crossed product groupoid $N\rtimes G\rightrightarrows N$ and (2) a transgression map from the singular cohomology $H^\ast(G_\bullet,\mathbb{Z})$ of the nerve of the groupoid $G$ to the singular cohomology $H^{\ast-1}\big((N\rtimes G)_\bullet,\mathbb{Z}\big)$ of the nerve of the crossed product groupoid $N\rtimes G$. The latter turns out to be identical to the transgression map obtained by Tu--Xu in their study of equivariant $K$-theory.
