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

Abstract

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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.

How to cite

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Garvín, 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

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

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