Differential <i>K</i>-theory, <i>η</i>-invariant, and localization

Liu, Bo; Ma, Xiaonan

doi:10.1016/j.crma.2019.09.006

Differential topology/Differential geometry

Differential K-theory, η-invariant, and localization
[K-théorie différentielle, invariant η et localisation]

Présenté par : the Editorial Board

Liu, Bo ¹ ; Ma, Xiaonan ²

¹ School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, PR China
² Université Paris-Diderot (Paris-7), UFR de mathématiques, case 7012, 75205 Paris cedex 13, France

Comptes Rendus. Mathématique, Tome 357 (2019) no. 10, pp. 803-813.

Résumé
Abstract

Nous établissons un résultat de comparaison de deux versions naturelles de l'invariant η équivariant par une formule locale. En combinant ce résultat avec une formule de localisation en K-théorie différentielle, nous obtenons une formule de localisation pour l'invariant η équivariant. Une étape importante est la construction d'une structure de pré-λ-anneau sur la K-théorie différentielle.

We establish a version of a localization formula for equivariant η-invariants by combining an extension of Goette's result on the comparison of two types of equivariant η-invariants and a localization formula in differential K-theory for $S^{1}$ -actions. An important step is to construct a pre-λ-ring structure in differential K-theory.

Reçu le : 2018-06-26
Accepté le : 2019-09-19
Publié le : 2019-10-01

DOI : 10.1016/j.crma.2019.09.006

Affiliations des auteurs :

Liu, Bo ¹ ; Ma, Xiaonan ²

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     title = {Differential {\protect\emph{K}-theory,} \protect\emph{\ensuremath{\eta}}-invariant, and localization},
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Liu, Bo; Ma, Xiaonan. Differential K-theory, η-invariant, and localization. Comptes Rendus. Mathématique, Tome 357 (2019) no. 10, pp. 803-813. doi : 10.1016/j.crma.2019.09.006. http://www.numdam.org/articles/10.1016/j.crma.2019.09.006/

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