Year: 2026
Type: preprint
Abstract: Let (X, g) be a compact smoothly stratified pseudomanifold equipped with an admissible iterated incomplete edge metric. We construct a canonical self-dual mezzoperversity on this class by taking the zero-energy limit of the low-energy scattering operator for the de Rham complex. For each singular stratum Y , this limit defines an endomorphism SY (0) of the Albin-Leichtnam-Mazzeo-Piazza trace bundle HY → Y . We prove that the associated involution field JY is fiberwise anti-symplectic for the Green form, smooth along the stratum, compatible with flat transport and incidence maps, stable under admissible deformations, and equivariant for duality. It follows that the fixed subbundles WY = Fix(JY ) determine a canonical mezzoperversity Wscatt. Invoking the Hodge-Fredholm theory of Albin-Leichtnam-Mazzeo-Piazza, we obtain Fredholmness of the resulting de Rham complex, identification with the corresponding intersection complex, and Poincaré duality in the self-dual case. The new input of the paper is the scattering construction and the proof of its compatibility properties; the Fredholm and sheaf-theoretic consequences are deduced only after the canonical datum has been established.
Source: HAL
Author: Luo, Jiaming
Institution: Kashi University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7140352586