This paper extends de Rham theory of smooth manifolds to exploded manifolds. Included are versions of Stokes’ theorem, de Rham cohomology, Poincaré duality, and integration along the fiber. The resulting de Rham cohomology theory of exploded manifolds is used in a separate paper (arXiv:1102.0158) to define Gromov-Witten invariants of exploded manifolds.
- De Rham cohomology
- Exploded manifolds