2003/07/09 by Weiping Zhang, Zhang, Weiping
Mathematics · Physics and Astronomy · #57F #58G #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Noncommutative and Quantum Gravity Theories #math.DG #math.KT #msc:57F #msc:58G
paper · pdf · doi:10.48550/arxiv.math/0307120
15 pages
arxiv created 2003/07/09 · openalex publication_date 2003/07/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the R/Z part of the analytically defined eta invariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a higher dimensional sphere. As a preliminary application, we discuss the relation with the Atiyah-Patodi-Singer R/Z index theorem for unitary flat vector bundles, and prove an R refinement in the case where the Dirac operator is replaced by the Signature operator. We also extend the above discussion to the case of eta invariants associated to Hermitian vector bundles with non-unitary connection, which are constructed by using a trick due to Lott.