Hodge cohomology of iterated fibred cusp metrics on Witt spaces

TL;DR

This paper establishes a correspondence between intersection cohomology and weighted $L^2$ cohomology for iterated fibred cusp metrics on Witt spaces, linking geometric analysis with topological invariants.

Contribution

It identifies intersection cohomology with weighted $L^2$ cohomology for a broad class of stratified spaces, extending previous results to iterated fibred cusp metrics on Witt spaces.

Findings

Intersection cohomology equals weighted $L^2$ cohomology for these metrics.

The $L^2$ cohomology matches middle perversity intersection cohomology on Witt spaces.

Provides a geometric-analytic interpretation of topological invariants.

Abstract

On a smoothly stratified space, we identify intersection cohomology of any given perversity with an associated weighted $L^2$ cohomology for iterated fibred cusp metrics on the smooth stratum. In particular given a Witt space, we identify the $L^2$ cohomology of iterated fibred cusp metrics with the middle perversity intersection cohomology of the corresponding stratified space.