Volume 22, issue 1 (2018)

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De Rham theory of exploded manifolds

Brett Parker

Geometry & Topology 22 (2018) 1–54
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.

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Keywords
exploded manifolds, de Rham cohomology
Mathematical Subject Classification 2010
Primary: 58A12, 55N35
References
Publication
Received: 11 February 2011
Revised: 29 January 2017
Accepted: 7 March 2017
Published: 31 October 2017
Proposed: Tomasz Mrowka
Seconded: Dan Abramovich, Jim Bryan
Authors
Brett Parker
Mathematical Sciences Institute
Australian National University
Canberra ACT
Australia