# Homotopical and operator algebraic twisted K-theory

## TL;DR

This paper establishes a multiplicative comparison between homotopical and operator algebraic twisted K-theory, enhancing understanding of their relationship and extending results to include multiplicative structures within an infinity-categorical framework.

## Contribution

It introduces a multiplicative comparison framework for twisted K-theory from homotopy theory and operator algebras, incorporating infinity-categorical perspectives.

## Key findings

- Established a multiplicative comparison between homotopical and operator algebraic twisted K-theory.
- Extended comparison results to include multiplicative structures in C*-algebra twisted K-theory.
- Interpreted results within the infinity-categorical setup for parametrized spectra.

## Abstract

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.