论文标题
dixmier-douady班级和同构小组的亚伯式扩展
The Dixmier-Douady class and an abelian extension of the homeomorphism group
论文作者
论文摘要
令$ x $为连接的拓扑空间，而$ c \ in \ mathrm {h}^2（x; \ mathbb {z}）$ a non-Zero cohomology类。 A $ \ MATHRM {HONEO}（X，C）$ - 捆绑包是一个带有纤维$ X $的纤维捆绑包，其结构组减少为$ \ mathrm {homeo}（homeo}（x，c）$ c $ c $ -c $ -preser-presererver-preserver-preserverving同源$ x $。如果$ \ mathrm {h}^1（x; \ mathbb {z}）= 0 $，则通过serre频谱序列定义了$ \ mathrm {homeo}（x，c）$ bundles的特征类。我们展示了用于FOLIADIAD $ \ MATHRM {HONEO}（X，C）$ - 捆绑的Universal Dixmier-douady类之间的关系与$ \ Mathrm {homeo}（homeo}（x，c）$的量规组扩展。此外，在某些假设下，我们在$ \ mathrm {homeo}（x，c）$上构建了一个中央$ s^1 $ extension和一个两组组的组，该$与dixmier-douady类相对应。
Let $X$ be a connected topological space and $c \in \mathrm{H}^2(X;\mathbb{Z})$ a non-zero cohomology class. A $\mathrm{Homeo}(X,c)$-bundle is a fiber bundle with fiber $X$ whose structure group reduces to the group $\mathrm{Homeo}(X,c)$ of $c$-preserving homeomorphisms of $X$. If $\mathrm{H}^1(X;\mathbb{Z}) = 0$, then a characteristic class for $\mathrm{Homeo}(X,c)$-bundles called the Dixmier-Douady class is defined via the Serre spectral sequence. We show a relation between the universal Dixmier-Douady class for foliated $\mathrm{Homeo}(X,c)$-bundles and the gauge group extension of $\mathrm{Homeo}(X,c)$. Moreover, under some assumptions, we construct a central $S^1$-extension and a group two-cocycle on $\mathrm{Homeo}(X,c)$ corresponding to the Dixmier-Douady class.
