deRham’s Theorem for Simplicial Complexes

  • Phillip Griffiths
  • John Morgan
Chapter
Part of the Progress in Mathematics book series (PM, volume 16)

Abstract

This chapter begins with a definition of the piecewise linear rational polynomial forms on a simplicial complex. These are shown to compute the usual rational singular cohomology (the p.l. deRham theorem). The construction is shown to be natural under subdivision of the simplicial complex and to produce a multiplicative isomorphism to singular cohomology. Connections with the usual smooth deRham theorem are given using piecewise smooth forms on a smoothly triangulated manifold.

Keywords

Manifold 

References

  1. 27.
    Whitney, H.: Geometric Integration Theory. Princeton Press, Princeton (1957)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Phillip Griffiths
    • 1
  • John Morgan
    • 2
  1. 1.Institute for Advanced StudyPrinceton UniversityPrincetonUSA
  2. 2.Simons Center for Geometry and PhysicsStony Brook UniversityStony BrookUSA

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