论文标题
较高扭曲的$ k $ - 理论中的计算
Computations in higher twisted $K$-theory
论文作者
论文摘要
较高扭曲的$ k $ - 理论是Ulrich Pennig介绍的扭曲$ K $的扩展，该理论捕获了所有同质理论的拓扑$ k $ - 理论。我们概述了他的表述和关键结果，并从拓扑角度重新制定了定义。然后，我们研究了$ k $的较高曲折的明确几何代表的方法 - 在特殊情况下，使用抓紧构建和班级分解时，被视为特殊案例的同一个学课。开发了Atiyah-Hirzebruch和Serre光谱序列，并获得了有关其差异的信息，并应用了这些较高扭曲的$ K $中的Mayer-Vietoris序列，以便为各种空间执行计算。
Higher twisted $K$-theory is an extension of twisted $K$-theory introduced by Ulrich Pennig which captures all of the homotopy-theoretic twists of topological $K$-theory in a geometric way. We give an overview of his formulation and key results, and reformulate the definition from a topological perspective. We then investigate ways of producing explicit geometric representatives of the higher twists of $K$-theory viewed as cohomology classes in special cases using the clutching construction and when the class is decomposable. Atiyah-Hirzebruch and Serre spectral sequences are developed and information on their differentials is obtained, and these along with a Mayer-Vietoris sequence in higher twisted $K$-theory are applied in order to perform computations for a variety of spaces.
