
doi: 10.1007/bf01077069
D. Sullivan's basic result in rational homotopy theory is that integration of differential forms whose coefficients are \(Q\)-polynomials in the barycentric coordinates of a simplicial complex \(X\) induces an isomorphism between the cohomology of the de Rham-Sullivan commutative differential graded algebra \(A^*(X)\) and the singular cohomology \(H^*(X;Q)\). The author sketches the proof of a similar result, for a finite complex \(X\), with emphasis on the ``coordinate ring'' \(A^ 0(X)\) and its associated de Rham complex, constructed in terms of Kähler differentials. The key role played by Sullivan's algebra of 0-forms \(A^ 0(X)\) in the homotopy theory of a finite complex \(X\) has been noticed by \textit{D. Kan} and \textit{E. Miller} [Topology 16, 193-197 (1977; Zbl 0367.55007) and Proc. Am. Math. Soc. 57, 337-339 (1976; Zbl 0332.58001)].
rational homotopy theory, Kähler differentials, Rational homotopy theory, simplicial complex, de Rham cohomology and algebraic geometry
rational homotopy theory, Kähler differentials, Rational homotopy theory, simplicial complex, de Rham cohomology and algebraic geometry
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 0 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
