Differential models for the Anderson dual to bordism theories and invertible QFT's, I

TL;DR

This paper develops new models for Anderson duals of stable tangential G-bordism theories and their differential extensions, providing mathematical support for their role in classifying invertible quantum field theories.

Contribution

It constructs explicit models for the Anderson duals to bordism theories, advancing the mathematical framework for understanding invertible QFTs and supporting Freed and Hopkins's conjecture.

Findings

Constructed models for Anderson duals to bordism theories.

Supported the conjecture relating these models to invertible QFTs.

Enhanced understanding of the mathematical structure of invertible quantum field theories.

Abstract

In this paper, we construct new models for the Anderson duals $(I\Omega^G)^*$ to the stable tangential $G$-bordism theories and their differential extensions. The cohomology theory $(I\Omega^G)^*$ is conjectured by Freed and Hopkins [FH21] to classify deformation classes of possibly non-topological invertible quantum field theories (QFT's). Our model is made by abstractizing certain properties of invertible QFT's, thus supporting their conjecture.