高扭曲$K$理论的计算
Computations in higher twisted $K$-theory
摘要：
高阶扭曲$K$ -理论是由Ulrich Pennig引入的扭曲$K$ -理论的扩展，它以几何的方式捕获了拓扑$K$ -理论的所有同伦理论扭曲。我们给出了一个概述，他的配方和关键成果，并重新定义从拓扑的角度来看。然后，我们调查的方式产生明确的几何代表的更高的扭曲的$K$ -理论被视为上同调类在特殊情况下使用的离合建设，当类是可分解的。Atiyah-Hirzebruch和Serre谱序列的发展和信息，他们的微分获得，这些随着迈尔-Vietoris序列在更高的扭曲$K$ -理论的应用，以执行各种空间的计算。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
