2009/01/04 by Charlotte Wahl, Wahl, Charlotte
Mathematics · #58J22 #58J32 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.DG #math.KT #msc:58J22 #msc:58J32
paper · pdf · doi:10.48550/arxiv.0901.0381
53 pages; some corrections and streamlining; references added
openalex publication_date 2009/01/04 · arxiv created 2012/05/01 · arxiv updated 2012/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove an Atiyah-Patodi-Singer index theorem for Dirac operators twisted by C*-vector bundles. We use it to derive a general product formula for eta-forms and to define and study new rho-invariants generalizing Lott's higher rho-form. The higher Atiyah-Patodi-Singer index theorem of Leichtnam-Piazza can be recovered by applying the theorem to Dirac operators twisted by the Mishenko-Fomenko bundle associated to the reduced C*-algebra of the fundamental group.