Quantitative towers in finite difference calculus approximating the continuum

R. Lawrence*, N. Ranade, D. Sullivan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Multivector fields and differential forms at the continuum level have respectively two commutative associative products, a third composition product between them and various operators like partial, d and '∗' which are used to describe many nonlinear problems. The point of this paper is to construct consistent direct and inverse systems of finite dimensional approximations to these structures and to calculate combinatorially how these finite dimensional models differ from their continuum idealizations. In a Euclidean background, there is an explicit answer which is natural statistically.

Original languageAmerican English
Pages (from-to)515-545
Number of pages31
JournalQuarterly Journal of Mathematics
Issue number1-2
StatePublished - 1 Jun 2021

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