Differential forms on orbifolds with corners

Jake P. Solomon, Sara B. Tukachinsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Motivated by symplectic geometry, we give a detailed account of differential forms and currents on orbifolds with corners, the pull-back and push-forward operations, and their fundamental properties. We work within the formalism where the category of orbifolds with corners is obtained as a localization of the category of étale proper groupoids with corners. Constructions and proofs are formulated in terms of the structure maps of the groupoids, avoiding the use of orbifold charts. The Fréchet space of differential forms on an orbifold and the dual space of currents are shown to be independent of which étale proper groupoid is chosen to represent the orbifold.

Original languageAmerican English
JournalJournal of Topology and Analysis
DOIs
StateAccepted/In press - 2023

Bibliographical note

Publisher Copyright:
© World Scientific Publishing Company.

Keywords

  • 2-category
  • Differential form
  • bicategory
  • category of fractions
  • integration over fibers
  • orbifold
  • étale proper groupoid

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