论文标题
关于拓扑布劳尔组的概括
On a generalization of the topological Brauer group
论文作者
论文摘要
在本文中，我们提出了包括较高同质信息的拓扑布劳尔组的一些概括，并包含经典信息作为直接求和。我们的方法基于某种类似捆绑的对象，称为``lax代数束''，该对象占据了``莫里塔束gerbes''和矩阵代数捆绑包之间的中间位置。本文的主要结果包括分类空间的同型类型的描述。获得的结果可以应用于扭曲的$ k $理论，因为宽松的代数束是``更高''的几何代表，''更高'的拓扑$ k $ - 具有有限顺序的曲折。 v.2：重大变化，尤其是在纸的下半年 v.3：为了澄清演示文稿，文本的重要部分已重写 v.4：重大更改，完全不同的方法与以前的版本进行比较 v.5：重大更改和更正 v.6：第3节添加了 v.7：实验室固定的等效性的定义 v.8：第3节已重写 v.9：备注3.2和第3.3小节中的一些解释 v.10在此版本中，我们省略了UHF代数方法；否则，已经进行了校正和澄清，在第4.3小节中，已经添加了实验室模块理论的概述 v.11：一些更正和澄清 v.12：定理6.2添加，较小的更正 v.13：一些加法（最重要的是第7节和备注3.5）
In the present paper we propose some generalization of the topological Brauer group that includes higher homotopical information and contains the classical one as a direct summand. Our approach is based on some kind of bundle-like objects called ``lax algebra bundles'' that occupy an intermediate position between ``Morita bundle gerbes'' and matrix algebra bundles. The main results of the paper include the descripion of the homotopy type of their classifying space. The obtained results can be applied to the twisted $K$-theory because the lax algebra bundles are geometric representatives of the ``higher'' twists of topological $K$-theory that have finite order. v.2: major changes, especially in the second half of the paper v.3: to clarify the presentation the significant part of the text has been rewritten v.4: major changes, completely different methods comparing with previous versions v.5: major changes and corrections v.6: section 3 added v.7: the definition of equivalence of LABs fixed v.8: section 3 has been rewritten v.9: remark 3.2 and some explanation in subsection 3.3 have been added v.10 in this version we omit the UHF algebra approach; otherwise, correction and clarifications have been made, in subsection 4.3 an outline of the theory of modules over LABs has been added v.11: some corrections and clarifications v.12: theorem 6.2 added, minor corrections v.13: some additions (the most important are section 7 and remark 3.5)
