1997/12/03 by Dave Auckly, Auckly, Dave
Computer Science · Mathematics · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.DG #math.GT
paper · pdf · doi:10.48550/arxiv.math/9712222
25 pages
arxiv created 1997/12/03 · openalex publication_date 1997/12/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper describes a topological method to compute the spectral flow of a family of twisted Dirac operators, it includes two detailed examples. Briefly, a formula of Atiyah, Patodi and Singer expresses the spectral flow in terms of Chern-Simons invariants and rho invariants. The first step is to construct a flat cobordism to a new bigger 3-manifold. The advantage of the new connection is that it is in the path component of a reducible connection. The second step is to calculate the effect of these operations on the invariants. The final step is an application of the G-signature theorem to compute the invariants.