Geometry & Topology

De Rham theory of exploded manifolds

Brett Parker

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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.

Article information

Geom. Topol., Volume 22, Number 1 (2018), 1-54.

Received: 11 February 2011
Revised: 29 January 2017
Accepted: 7 March 2017
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58A12: de Rham theory [See also 14Fxx] 55N35: Other homology theories

exploded manifolds de Rham cohomology


Parker, Brett. De Rham theory of exploded manifolds. Geom. Topol. 22 (2018), no. 1, 1--54. doi:10.2140/gt.2018.22.1.

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