Demonstrates an additivity axiom for torsion forms in a smooth fibration, suggesting implications for analytical torsion and geometric topology.
We consider a smooth fibration equipped with a flat complex vector bundle and a hypersurface cutting the fibration into two pieces. Our main result is a gluing formula relating the Bismut-Lott analytic torsion form of the whole fibration to that of each piece. This result solves a conjecture proposed at a conference in Göttingen in 2003. This result also leads to a higher Cheeger-Müller/Bismut-Zhang theorem. Our approach combines an adiabatic limit along the normal direction of the hypersurface and a Witten-type deformation on the flat vector bundle.
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Puchol et al. (2026) studied this question.
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