Geometry & Topology

De Rham theory of exploded manifolds

Brett Parker

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513774909

Digital Object Identifier
doi:10.2140/gt.2018.22.1

Mathematical Reviews number (MathSciNet)
MR3720340

Zentralblatt MATH identifier
1380.58001

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

Keywords
exploded manifolds de Rham cohomology

Citation

Parker, Brett. De Rham theory of exploded manifolds. Geom. Topol. 22 (2018), no. 1, 1--54. doi:10.2140/gt.2018.22.1. https://projecteuclid.org/euclid.gt/1513774909


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References

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