Cohomology of flat currents on definable pseudomanifolds

TL;DR

This paper demonstrates that the cohomology of flat currents on definable pseudomanifolds in polynomially bounded o-minimal structures aligns with intersection cohomology in the top perversity, bridging geometric analysis and topological invariants.

Contribution

It establishes an isomorphism between flat current cohomology and intersection cohomology in a specific o-minimal setting, providing a new link between analysis and topology.

Findings

Cohomology of flat currents matches intersection cohomology in the top perversity.

Validates the use of flat currents in o-minimal geometric contexts.

Enhances understanding of topological invariants in definable pseudomanifolds.

Abstract

We show that the cohomology of flat currents on definable pseudomanifolds in polynomially bounded o-minimal structures is isomorphic to its intersection cohomology in the top perversity.