De Rham theory of exploded manifolds

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.

57 pages. v4: Post-publication update fixing an error in the computation of compactly supported cohomology of a coordinate chart. An additional assumption that a polytope was simplicial at infinity was required. As a consequence, this additional assumption is also required for the integration pairing to be a perfect pairing. See Appendix for further details

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• Pseudoholomorphic Curves Relative to a Normal Crossings Symplectic Divisor: Compactification