In this paper we present an approximation to the de Rham theorem for simplicial sets with any coefficients based, using simplicial techniques, on Poincaré's lemma and q-extendability.
@article{bwmeta1.element.bwnjournal-article-bcpv45i1p169bwm, author = {Garv\'\i n, Antonio and Lechuga, Luis and Murillo, Aniceto and Mu\~noz, Vicente and Viruel, Antonio}, title = {An extension of Miller's version of the de Rham Theorem with any coefficients}, journal = {Banach Center Publications}, volume = {43}, year = {1998}, pages = {169-176}, zbl = {0945.55007}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv45i1p169bwm} }
Garvín, Antonio; Lechuga, Luis; Murillo, Aniceto; Muñoz, Vicente; Viruel, Antonio. An extension of Miller's version of the de Rham Theorem with any coefficients. Banach Center Publications, Tome 43 (1998) pp. 169-176. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv45i1p169bwm/
[000] [1] H. Cartan, Théories cohomologiques, Invent. Math. 35 (1976), 261-271. | Zbl 0334.55005
[001] [2] B. Cenkl, Cohomology operations from higher products in the de Rham complex, Pacific Journal of Math. 140 1 (1989), 21-33.
[002] [3] Y. Félix, S. Halperin and J. C. Tomas, Rational Homotopy Theory, Preprint Univ. of Toronto, version 96.2, (1996).
[003] [4] S. Halperin, Lectures on minimal models, Mémoire de la Soc. Math. de France, 9/10 (1983). | Zbl 0536.55003
[004] [5] P. May, Simplicial objects in algebraic topology, Van Nostrand, 1967.
[005] [6] E. Y. Miller, De Rham cohomology with arbitrary coefficients, Topology 17 (1978), 193-203. | Zbl 0386.55011
[006] [7] D. Quillen, Rational homotopy theory, Annals of Math. 90 (1969), 205-295. | Zbl 0191.53702
[007] [8] D. Sullivan, Infinitesimal Computations in Topology, Publ. de l'I.H.E.S. 47 (1978), 269-331.
[008] [9] R. Swan, Thom's theory of differential forms on simplicial sets, Topology 14 (1975). 271-273. | Zbl 0319.58004