Adiabatic limit, Witten deformation and analytic torsion forms

2020/09/29 by Martin Puchol, Puchol, Martin, Yeping Zhang +3 · 1 citation
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Algebra and Geometry #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.2009.13925

Abstract

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 confirms a conjecture proposed in a conference in Goettingen in 2003. Our approach combines an adiabatic limit along the normal direction of the hypersurface and a Witten type deformation on the flat vector bundle. Due to disagreement among authors, author Zhang unilaterally decides to never publish this paper. If you saw this paper published somewhere, it must be without Zhang's approvement.

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• A comparison between the Bismut-Lott torsion and the Igusa-Klein torsion

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