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arXiv · 2510.27286

Differential Models for the Anderson Dual to Twisted $\mathrm{Spin}^c$-Bordism and a Twisted Anomaly Map

Fei Han·Yuanchu Li
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Abstract

We construct differential models for degree-3 twisted $\mathrm{Spin}^c$-bordism and for its Anderson dual. The model for the differential Anderson dual is based on the framework of Yamashita--Yonekura. Using these differential models, we define a twisted anomaly map from differential twisted $K$-theory with inverse twist to the differential Anderson dual of twisted $\mathrm{Spin}^c$-bordism. The construction is described geometrically in terms of bundle gerbes, gerbe modules, and reduced eta-invariants of Dirac operators associated to the twisted data. Conceptually, this map is expected to be related to the anomalies of twisted $1|1$-dimensional supersymmetric field theories, in line with the perspectives of Stolz--Teichner and Freed--Hopkins.

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Fei Han, Yuanchu Li. 2025-10-31. Differential Models for the Anderson Dual to Twisted $\mathrm{Spin}^c$-Bordism and a Twisted Anomaly Map. https://arxiv.org/abs/2510.27286

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