Families of equivariant immersions and analytic torsion forms
type: Item
instance of: scholarly article
title: Families of equivariant immersions and analytic torsion forms
zbMATH Open document ID: 1010.32015
DOI: 10.1016/S1631-073X(02)02372-5
author: Jean-Michel Bismut
author: Xiaonan Ma
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2003-05-06T00:00:00Z
review text: The authors extend -- in the equivariant framework -- some results of \textit{J. M. Bismut} [Holomorphic families of immersions and higher order analytic torsion forms, Astérisque 244 (1997; Zbl 0899.32013)]. Namely, they study the behavior of the equivariant holomorphic analytic torsion forms constructed in a paper by \textit{X. Ma} [Ann. Inst. Fourier 50, 1539-1588 (2000; Zbl 0964.58025)]. The resulting formulas generalize those of \textit{J.-M. Bismut} [J. Differ. Geom. 41, 53-157 (1995; Zbl 0826.32024)] to arbitrary dimension.
Mathematics Subject Classification ID: 32Q40
Mathematics Subject Classification ID: 58J52
zbMATH DE Number: 1777385
zbMATH Keywords: equivariant immersions
zbMATH Keywords: holomorphic analytic torsion form
reviewed by: Witold Mozgawa
MaRDI profile type: Publication
cites work: The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs
cites work: Superconnection currents and complex immersions
cites work: Q4312301
cites work: Equivariant immersions and Quillen metrics
cites work: Q4393472
cites work: Analytic torsion and holomorphic determinant bundles. I: Bott-Chern forms and analytic torsion. II: Direct images and Bott-Chern forms. III: Quillen metrics on holomorphic determinants
cites work: Q5288191
cites work: Complex immersions and Quillen metrics
cites work: Holomorphic immersions and equivariant torsion forms
cites work: Analytic torsion and the arithmetic Todd genus. (With an appendix by D. Zagier)
cites work: An arithmetic Riemann-Roch theorem
cites work: A fixed point formula of Lefschetz type in Arakelov geometry. I: Statement and proof
cites work: Submersions and equivariant Quillen metrics
cites work: Conjectures on the logarithmic derivatives of Artin \(L\)-functions at negative integers
cites work: Determinants of Cauchy-Riemann operators on a Riemann surface
cites work: Superconnections and the Chern character
cites work: Analytic torsion for complex manifolds
cites work: An Adams-Riemann-Roch theorem in Arakelov geometry
description: scientific article; zbMATH DE number 1777385