English

Exploded Manifolds

Symplectic Geometry 2017-09-14 v5

Abstract

This paper provides an introduction to exploded manifolds. The category of exploded manifolds is an extension of the category of smooth manifolds with an excellent holomorphic curve theory. Each exploded manifold has a tropical part which is a union of convex polytopes glued along faces. Exploded manifolds are useful for defining and computing Gromov-Witten invariants relative to normal crossing divisors, and using tropical curve counts to compute Gromov-Witten invariants.

Keywords

Cite

@article{arxiv.0910.4201,
  title  = {Exploded Manifolds},
  author = {Brett Parker},
  journal= {arXiv preprint arXiv:0910.4201},
  year   = {2017}
}

Comments

v4 Post-publication(!) correction to Definition 3.1 of an abstract exploded space. See footnotes on pages 14 and 22. v5: I corrected the singular of `strata' to `stratum' throughout

R2 v1 2026-06-21T14:01:49.773Z