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.
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