Equivariant immersions and Quillen metrics
type: Item
instance of: scholarly article
title: Equivariant immersions and Quillen metrics
zbMATH Open document ID: 0826.32024
author: Jean-Michel Bismut
published in: Journal of Differential Geometry
publication date: 1995-11-12T00:00:00Z
review text: The author and \textit{G. Lebeau} [Publ. Math., Inst. Hautes Etud. Sci. 74, 1-297 (1991; Zbl 0784.32010)] proved an integral formula being an important step in the proof of Gillet and Soulé of the Riemann-Roch Theorem in Arakelov geometry. In the present paper the author extends the formula to the equivariant case. More exactly he constructs Quillen metrics on the equivariant determinant of the cohomology of a holomorphic vector bundle with respect to the action of a compact group \(G\) and he calculates the behaviour of the equivariant Quillen metric by immersions. The author considers his result as a new block in the construction of an Arakelov theory to be in an equivariant context. At the beginning of the paper the author describes the complications which arise in generalising the techniques and arguments from the previous paper to the present case. The results of this paper were announced in C. R. Acad. Sci., Paris, Sér. I 316, No. 8, 827-832 (1993; Zbl 0773.53026).
Mathematics Subject Classification ID: 32L10
Mathematics Subject Classification ID: 32C30
Mathematics Subject Classification ID: 32J18
Mathematics Subject Classification ID: 32M05
Mathematics Subject Classification ID: 53C56
zbMATH DE Number: 761186
zbMATH Keywords: analytic torsion
zbMATH Keywords: superconnection
zbMATH Keywords: Quillen metrics
zbMATH Keywords: equivariant determinant
zbMATH Keywords: cohomology
zbMATH Keywords: holomorphic vector bundle
zbMATH Keywords: immersions
reviewed by: Krzysztof Dabrowski
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214456007
OpenAlex ID: W1557752050
Wikidata QID: Q115178731
DOI: 10.4310/JDG/1214456007
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description: scientific article; zbMATH DE number 761186