A Maximal Cgm-type L 2 De Rham Theory for Stratified Pseudomanifolds With Iterated Incomplete Edge Metrics
Year: 2026
Type: preprint
Abstract: On a smoothly stratified pseudomanifold equipped with an iterated incomplete edge (iie) metric, the de Rham differential admits many closed L 2 extensions, so any general Cheeger-Goresky-MacPherson statement must be parameterized by ideal boundary conditions (mezzoperversities). Building on the framework of Albin-Leichtnam-Mazzeo-Piazza, we associate to each mezzoperversity W a Fredholm L 2 de Rham complex on X reg whose cohomology identifies with a Deligne-type intersection cohomology IH • W (X) and is invariant under changes of suitably scaled iie metrics within a fixed quasi-isometry class. We characterize Cheeger spaces (those admitting a selfdual W), for which Poincaré duality holds and, in dimension 4ℓ, the analytic signature agrees with Banagl's topological signature. We also exhibit an obstruction to a functorial canonical "middle" choice of W on the full iie class. Finally, in the projective Fubini-Study setting, Kähler polarization provides additional structure yielding a canonical middle identification H • (2) (X reg , dcan) ∼ = IH • m(X ) on complex projective varieties.
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: W7139519438