Using the framework for multiplicative parametrized homotopy theory introduced in joint work with C. Schlichtkrull, we produce a multiplicative comparison between the homotopical and operator algebraic constructions of twisted K-theory, both in the real and complex case. We also improve several comparison results about twisted K-theory of C*-algebras to include multiplicative structures. Our results can also be interpreted in the infinity-categorical setup for parametrized spectra.

中文翻译：

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同伦和算子代数扭曲 K 理论

使用与 C. Schlichtkrull 合作引入的乘法参数化同伦理论框架，我们在真实和复杂情况下对扭曲 K 理论的同伦和算子代数构造进行乘法比较。我们还改进了关于 C*-代数的扭曲 K 理论的几个比较结果，以包括乘法结构。我们的结果也可以在参数化光谱的无穷大分类设置中进行解释。