de Rham theorem with cubical forms

Bohumil Cenkl and Richard D. Porter

Vol. 112 (1984), No. 1, 35–48

DOI: 10.2140/pjm.1984.112.35

Abstract

With a simplicial complex X there is associated a commutative differential graded algebra of polynomial differential forms T(X) together with a filtration T^∗,q(X) ⊂ T^∗,q+1(X) in each degree ^∗. T^∗,q(X) is a differential graded module over the subring of the rationals Z[,…,]. The deRham theorem for such a complex T(X) is proved. We have demonstrated elsewhere that the refined deRham complex T(X) makes it possible to substantially refine most of the results of the rational homotopy theory. In particular we defined the homotopy category of C-N spaces which is equivalent to an algebraic homotopy category of (N − 1) connected free commutative differential graded algebras over the integers, satisfying a simple algebraic condition on cohomology.

Mathematical Subject Classification 2000

Primary: 55N10

Secondary: 55U15, 58A12, 58C35

Milestones

Received: 13 March 1979

Revised: 16 February 1983

Published: 1 May 1984