Adiabatic limit, Bismut-Freed connection, and the real analytic torsion form

2008/07/24 by Xianzhe Dai, Dai, Xianzhe, Weiping Zhang +1
Mathematics · #58GXX #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory #math.DG #msc:58GXX

paper · pdf · doi:10.48550/arxiv.0807.3782

arxiv created 2008/07/24 · openalex publication_date 2008/07/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a complex flat vector bundle over a fibered manifold, we consider the 1-parameter family of certain deformed sub-signature operators introduced by Ma-Zhang. We compute the adiabatic limit of the Bismut-Freed connection associated to this family and show that the Bismut-Lott analytic torsion form shows up naturally under this procedure.

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