English

De Rham theory of exploded manifolds

Differential Geometry 2020-11-24 v4

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.

Keywords

Cite

@article{arxiv.1003.1977,
  title  = {De Rham theory of exploded manifolds},
  author = {Brett Parker},
  journal= {arXiv preprint arXiv:1003.1977},
  year   = {2020}
}

Comments

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

R2 v1 2026-06-21T14:55:44.617Z