Differential K-theory and localization formula for η-invariants

• 成果类型: Article
• 署名作者: Liu, Bo; Ma, Xiaonan
• 署名单位: East China Normal University; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Chinese Academy of Sciences; University of Science & Technology of China, CAS
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-00973-8
• 发表日期: 2020
• 页码: 545-613
• 关键词: fixed-point formula; riemann-roch theorem; lefschetz type; spectral asymmetry; dirac operators; real embeddings; index theorem; equivariant; families; torsion

摘要

In this paper we obtain a localization formula in differential K-theory for S-1-actions. We establish a localization formula for equivariant eta-invariants by combining this result with our extension of Goette's result on the comparison of two types of equivariant eta-invariants. An important step in our approach is to construct a pre-lambda-ring structure in differential K-theory.