1996/08/08 by Xianzhe Dai, Dai, Xianzhe, Weiping Zhang +1
Mathematics · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #dg-ga #math.DG
paper · pdf · doi:10.48550/arxiv.dg-ga/9608002
Latex, 35 pages
arxiv created 1996/08/08 · openalex publication_date 1996/08/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a continuous curve of families of Dirac type operators we define a higher spectral flow as a K-group element. We show that this higher spectral flow can be computed analytically by \heta-forms, and is related to the family index in the same way as the spectral flow is related to the index. We introduce a notion of Toeplitz family and relate its index to the higher spectral flow. Applications to family indices for manifolds with boundary are also given.