# An extension of Miller's version of the de Rham Theorem with any coefficients

Antonio Garvín; Luis Lechuga; Aniceto Murillo; Vicente Muñoz; Antonio Viruel

Banach Center Publications (1998)

- Volume: 45, Issue: 1, page 169-176
- ISSN: 0137-6934

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topGarvín, Antonio, et al. "An extension of Miller's version of the de Rham Theorem with any coefficients." Banach Center Publications 45.1 (1998): 169-176. <http://eudml.org/doc/208901>.

@article{Garvín1998,

abstract = {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.},

author = {Garvín, Antonio, Lechuga, Luis, Murillo, Aniceto, Muñoz, Vicente, Viruel, Antonio},

journal = {Banach Center Publications},

keywords = {commutative cochain problem; de Rham theorem; simplicial set; polynomial algebra},

language = {eng},

number = {1},

pages = {169-176},

title = {An extension of Miller's version of the de Rham Theorem with any coefficients},

url = {http://eudml.org/doc/208901},

volume = {45},

year = {1998},

}

TY - JOUR

AU - Garvín, Antonio

AU - Lechuga, Luis

AU - Murillo, Aniceto

AU - Muñoz, Vicente

AU - Viruel, Antonio

TI - An extension of Miller's version of the de Rham Theorem with any coefficients

JO - Banach Center Publications

PY - 1998

VL - 45

IS - 1

SP - 169

EP - 176

AB - 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.

LA - eng

KW - commutative cochain problem; de Rham theorem; simplicial set; polynomial algebra

UR - http://eudml.org/doc/208901

ER -

## References

top- [1] H. Cartan, Théories cohomologiques, Invent. Math. 35 (1976), 261-271. Zbl0334.55005
- [2] B. Cenkl, Cohomology operations from higher products in the de Rham complex, Pacific Journal of Math. 140 1 (1989), 21-33.
- [3] Y. Félix, S. Halperin and J. C. Tomas, Rational Homotopy Theory, Preprint Univ. of Toronto, version 96.2, (1996).
- [4] S. Halperin, Lectures on minimal models, Mémoire de la Soc. Math. de France, 9/10 (1983). Zbl0536.55003
- [5] P. May, Simplicial objects in algebraic topology, Van Nostrand, 1967.
- [6] E. Y. Miller, De Rham cohomology with arbitrary coefficients, Topology 17 (1978), 193-203. Zbl0386.55011
- [7] D. Quillen, Rational homotopy theory, Annals of Math. 90 (1969), 205-295. Zbl0191.53702
- [8] D. Sullivan, Infinitesimal Computations in Topology, Publ. de l'I.H.E.S. 47 (1978), 269-331.
- [9] R. Swan, Thom's theory of differential forms on simplicial sets, Topology 14 (1975). 271-273. Zbl0319.58004

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