The index formula for families of Dirac type operators on pseudomanifolds

2017/12/22 by Pierre Albin, Albin, Pierre, Jesse Gell‐Redman +1 · 3 citations
Mathematics · Physics and Astronomy · #58J20 32S60 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1712.08513

openalex publication_date 2017/12/22 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We study families of Dirac-type operators, with compatible perturbations, associated to wedge metrics on stratified spaces. We define a closed domain and, under an assumption of invertible boundary families, prove that the operators are self-adjoint and Fredholm with compact resolvents and trace-class heat kernels. We establish a formula for the Chern character of their index.

Cited by

• The G-signature Theorem on Witt spaces
• Analysis on fibred cusp spaces
• Géométrie à l'infini des variétés hyperkählériennes toriques

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