Non- commutative differential forms and Steenrod operations. (Formes differentielles non commutatives et operations de Steenrod.) (French) Zbl 0834.55011
The author gives a short construction of the Steenrod operations. The method requires models for Eilenberg-MacLane spaces which have well- behaved products and actions by symmetric groups. Such models can be obtained from infinite symmetric products of spheres, or by using non- commutative differential forms. By using the latter method, the author associates complexes of differential forms with symmetric group actions to any simplicial set. These complexes are quasi-isomorphic to the non- commutative de Rham complex and they determine the Steenrod operations. The author suggests that they provide good algebraic models for homotopy types.
Reviewer: R.J.Steiner (Glasgow)
MSC:
55S05 | Primary cohomology operations in algebraic topology |
58A10 | Differential forms in global analysis |
18G55 | Nonabelian homotopical algebra (MSC2010) |
55U35 | Abstract and axiomatic homotopy theory in algebraic topology |
55N35 | Other homology theories in algebraic topology |