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

Abstract

In this paper, we construct new models for the Anderson duals $(I{\Omega }^G{)}^{\ast }$ to the stable tangential $G$-bordism theories and their differential extensions. The cohomology theory $(I{\Omega }^G{)}^{\ast }$ 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.

60 pages, 1 figures. The content of this article has been greatly changed and improved from the first version (v1). The results of v1 are contained in Sections 3 and 4 of the current version. See Remark 1.20 for details

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