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ASYMPTOTIC TORSION AND TOEPLITZ OPERATORS

Part of: Partial differential equations on manifolds; differential operators

Published online by Cambridge University Press:  11 June 2015

Jean-Michel Bismut ,
Xiaonan Ma  and
Weiping Zhang
Jean-Michel Bismut
Affiliation:
Département de Mathématique, Université Paris-Sud, Bâtiment 425, F-91405 Orsay, France (Jean-Michel.Bismut@math.u-psud.fr)
Xiaonan Ma
Affiliation:
Université Paris 7, UFR de Mathématiques, Case 7012, F-75205 Paris Cedex 13, France (xiaonan.ma@imj-prg.fr)
Weiping Zhang
Affiliation:
Chern Institute of Mathematics & LPMC, Nankai University, Tianjin 300071, PR China (weiping@nankai.edu.cn)
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Abstract

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We use Toeplitz operators to evaluate the leading term in the asymptotics of the analytic torsion forms associated with a family of flat vector bundles $F_{p}$ . For $p\in \mathbf{N}$ , the flat vector bundle $F_{p}$ is the direct image of $L^{p}$ , where $L$ is a holomorphic positive line bundle on the fibres of a flat fibration by compact Kähler manifolds. The leading term of the analytic torsion forms is the integral along the fibre of a locally defined differential form.

Keywords

index theory and related fixed point theoremsdeterminants and determinant bundlesanalytic torsion

MSC classification

Primary: 58J20: Index theory and related fixed point theorems 58J52: Determinants and determinant bundles, analytic torsion
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 16 , Issue 2 , April 2017 , pp. 223 - 349
Copyright
© Cambridge University Press 2015 

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