Local index theory and higher analytic torsion
type: Item
instance of: scholarly article
title: Local index theory and higher analytic torsion
zbMATH Open document ID: 0982.58016
author: Jean-Michel Bismut
published in: Documenta Mathematica
publication date: 1998-08-24T00:00:00Z
full work available at URL: https://eudml.org/doc/231023
full work available at URL: Bismut.MAN.html
review text: Summary: We report on the construction of secondary invariants in connection with the Atiyah-Singer index theorem for families, and the Theorem of Riemann-Roch-Grothendieck. The local families index theorem plays an important role in the construction. In complex geometry, the corresponding objects are the analytic torsion forms and the analytic torsion currents. These objects exhibit natural functorial properties with respect to composition of maps. Gillet and Soulé have used these objects to prove a Riemann-Roch theorem in Arakelov geometry. Also we state a Riemann-Roch theorem for flat vector bundles, and report on the construction of corresponding higher analytic torsion forms.
Mathematics Subject Classification ID: 58J20
Mathematics Subject Classification ID: 58J52
Mathematics Subject Classification ID: 32L10
zbMATH DE Number: 1194145
zbMATH Keywords: sheaves and cohomology of sections of holomorphic vector bundles
zbMATH Keywords: characteristic classes and numbers
zbMATH Keywords: secondary invariant
zbMATH Keywords: Atiyah-Singer index theorem
zbMATH Keywords: theorem of Riemann-Roch-Grothendieck
zbMATH Keywords: local families index theorem
zbMATH Keywords: analytic torsion forms
zbMATH Keywords: analytic torsion currents
zbMATH Keywords: flat vector bundles
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1194145