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 -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.
Accepted:
Published online:
Bo Liu 1; Xiaonan Ma 2
@article{CRMATH_2019__357_10_803_0,
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},
volume = {357},
number = {10},
year = {2019},
doi = {10.1016/j.crma.2019.09.006},
language = {en},
}
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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.09.006/
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