2024/03/01 by Peter Hochs, Hochs, Peter, Aquerman Yanes +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Numerical methods in inverse problems #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2403.00575
openalex publication_date 2024/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the setting of a proper, cocompact action by a locally compact, unimodular group G on a Riemannian manifold, we construct equivariant spectral flow of paths of Dirac-type operators. This takes values in the K-theory of the group C^*-algebra of G. In the case where G is the fundamental group of a compact manifold, the summation map maps equivariant spectral flow on the universal cover to classical spectral flow on the base manifold. We obtain "index equals spectral flow" results. In the setting of a smooth path of G-invariant Riemannian metrics on a G-spin manifold, we show that the equivariant spectral flow of the corresponding path of spin Dirac operators relates delocalised η-invariants and ρ-invariants for different positive scalar curvature metrics to each other.