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The index formula for families of Dirac type operators on pseudomanifolds

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arxiv 1712.08513 v1 pith:C35W5ZRX submitted 2017-12-22 math.DG math.APmath.GT

Pierre Albin , Jesse Gell-Redman This is my paper · ORCID
classification math.DGmath.APmath.GT
keywords familiesoperatorsformulaindexassociatedassumptionboundarycharacter
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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.

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  1. Extensions and Applications of Bredon's Trick in Geometric and Topological Contexts

    math.DG 2025-07 reject novelty 2.0 of 10

    The paper claims Bredon's trick yields new results in Verona cohomology, Ricci flow singularity classification, and mapper stability, but the proofs are invalid or circular.

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