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arXiv · 2512.18602

Adiabatic Limit and Analytic Torsion of Vector Bundles

Xianzhe Dai·Debin Liu
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Abstract

For a vector bundle $E^{n+k}$ over a closed manifold $M^n$ with $k$ even and $n$ odd, we equip the metric with an adiabatic parameter, and prove that the index of $E$ is the same as the index of $M$. We also introduce an analog of analytic torsion on $E$ using the Witten Laplacian. Moreover, we prove that the Quillen metric associated with this analytic torsion coincides with that of $M$.

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Xianzhe Dai, Debin Liu. 2025-12-21. Adiabatic Limit and Analytic Torsion of Vector Bundles. https://arxiv.org/abs/2512.18602

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