Comptes Rendus
Differential topology/Differential geometry
Differential K-theory, η-invariant, and localization
Comptes Rendus. Mathématique, Volume 357 (2019) no. 10, pp. 803-813.

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 S1-actions. An important step is to construct a pre-λ-ring structure in differential K-theory.

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.

Published online:
DOI: 10.1016/j.crma.2019.09.006

Bo Liu 1; Xiaonan Ma 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
     author = {Bo Liu and Xiaonan Ma},
     title = {Differential {\protect\emph{K}-theory,} \protect\emph{\ensuremath{\eta}}-invariant, and localization},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {803--813},
     publisher = {Elsevier},
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     number = {10},
     year = {2019},
     doi = {10.1016/j.crma.2019.09.006},
     language = {en},
AU  - Bo Liu
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TI  - Differential K-theory, η-invariant, and localization
JO  - Comptes Rendus. Mathématique
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PB  - Elsevier
DO  - 10.1016/j.crma.2019.09.006
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%A Xiaonan Ma
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Bo Liu; Xiaonan Ma. Differential K-theory, η-invariant, and localization. Comptes Rendus. Mathématique, Volume 357 (2019) no. 10, pp. 803-813. doi : 10.1016/j.crma.2019.09.006.

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