De Rham theory of exploded manifolds

TL;DR

This paper extends classical de Rham theory to exploded manifolds, establishing foundational results like Stokes' theorem and Poincare duality, and applying these to define Gromov-Witten invariants.

Contribution

It introduces a de Rham cohomology framework for exploded manifolds, enabling new geometric and topological analyses.

Findings

Established Stokes' theorem for exploded manifolds

Defined de Rham cohomology in this new setting

Applied the theory to Gromov-Witten invariants

Abstract

This paper extends de Rham theory of smooth manifolds to exploded manifolds. Included are versions of Stokes' theorem, De Rham cohomology, Poincare duality, and integration along the fiber. The resulting cohomology theory is used to define Gromov Witten invariants of exploded manifolds in a separate paper.