Abstract and classical Hodge-de Rham theory

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)91-111
Journal / PublicationAnalysis and Applications
Volume10
Issue number1
Publication statusPublished - Jan 2012

Abstract

In previous work, with Bartholdi and Schick [1], the authors developed a Hodgede Rham theory for compact metric spaces, which defined a cohomology of the space at a scale α. Here, in the case of Riemannian manifolds at a small scale, we construct explicit chain maps between the de Rham complex of differential forms and the L 2 complex at scale α, which induce isomorphisms on cohomology. We also give estimates that show that on smooth functions, the Laplacian of [1], when appropriately scaled, is a good approximation of the classical Laplacian. © 2012 World Scientific Publishing Company.

Research Area(s)

  • cohomology, de Rham theory, Hodge theory

Citation Format(s)

Abstract and classical Hodge-de Rham theory. / Smale, Nat; Smale, Steve.
In: Analysis and Applications, Vol. 10, No. 1, 01.2012, p. 91-111.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review