2019/05/31 by Phillip Andreae, Andreae, Phillip
Computer Science · Mathematics · Physics and Astronomy · #58J10 #58J28 #58J35 #58J52 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Topological and Geometric Data Analysis #math.DG #math.GT #msc:58J10 #msc:58J28 #msc:58J35 #msc:58J52
paper · pdf · doi:10.48550/arxiv.1905.13721
33 pages; same results as v1, with significant edits to the exposition
openalex publication_date 2019/05/31 · arxiv created 2021/07/30 · arxiv updated 2021/08/02 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
We introduce multi-torsion, a spectral invariant generalizing Ray-Singer analytic torsion. We define multi-torsion for compact manifolds with a certain local geometric product structure that gives a bigrading on differential forms. We prove that multi-torsion is metric-independent in a suitable sense. Our definition of multi-torsion is inspired by an interpretation of each of analytic torsion and the eta invariant as a regularized integral of a closed differential form on a space of metrics on a vector bundle or on a space of elliptic operators. We generalize the Stokes' theorem argument explaining the dependence of torsion and eta on the geometric data used to define them to the local product setting to prove our metric-independence theorem for multi-torsion.