Analytic surgery and gluing of the Bismut-Lott torsion form and eta form

2022/05/27 by Bing Kwan So, So, Bing Kwan
Mathematics · #58J28 #58J52 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2205.13979

openalex publication_date 2022/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a fiber bundle with closed connected fibers, and a family of separating hypersurfaces, we study the behavior of the Bismut-Lott analytic torsion form, and the eta form for a duality bundle, under analytic surgery in the sense of Hassell, Mazzeo and Melrose. We find that under the surgery limit, the rescaled heat kernel is non-singular, while both the Bismut-Lott analytic torsion form and eta form can be written as the sum of a logarithmic term, which satisfies the Igusa additivity property, the b- Bismut-Lott analytic torsion form (respectively the b- eta form), and an error term coming from the reduced normal operator. Hence we obtain a gluing formula for these invariants.

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