Geodesic
De Rham theory of exploded manifolds
Parker, Brett1
1 Mathematical Sciences Institute, Australian National University, Canberra ACT, Australia
Geometry & topology, Tome 22 (2018) no. 1, pp. 1-54.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/gt.2018.22.1
Classification : 58A12, 55N35
Keywords: exploded manifolds, de Rham cohomology

Parker, Brett 1

1 Mathematical Sciences Institute, Australian National University, Canberra ACT, Australia 
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Parker, Brett. De Rham theory of exploded manifolds. Geometry & topology, Tome 22 (2018) no. 1, pp. 1-54. doi : 10.2140/gt.2018.22.1. http://geodesic.mathdoc.fr/articles/10.2140/gt.2018.22.1/

[1] R Bott, L W Tu, Differential forms in algebraic topology, 82, Springer (1982) | DOI

[2] B Parker, Exploded fibrations, from: "Proceedings of Gökova Geometry–Topology Conference 2006" (editors S Akbulut, T Önder, R J Stern), GGT (2007) 52

[3] B Parker, Exploded manifolds, Adv. Math. 229 (2012) 3256 | DOI

[4] B Parker, Integral counts of pseudo-holomorphic curves, preprint (2013)

[5] B Parker, Holomorphic curves in exploded manifolds: compactness, Adv. Math. 283 (2015) 377 | DOI

[6] L Ramshaw, J Basch, Orienting transverse fiber products, technical report (2009)

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