A propos de conjectures de Serre et Sullivan |
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Authors: | Jean Lannes Lionel Schwartz |
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Institution: | (1) Unité Associée au CNRS no 169, Centre de Mathématiques de l'Ecole Polytechnique, Plateau de Palaiseau, F-91128 Palaiseau Cedex;(2) Bât. 425 Mathématiques, Unité Associée au CNRS LP 13, Université de Paris XI, F-91405 Orsay Cedex |
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Abstract: | Summary We first give a new proof of a conjecture of J.-P. Serre on the homotopy of finite complexes, which was recently proved by C. McGibbon and J. Neisendorfer. The emphasis is on a property of the mod. 2 homology of certain spaces: their quasi-boundedness as right modules over the Steenrod algebra. This property is preserved when one goes from a simply connected space to its loop space and also when one takes a covering of anH-space. Then we show that this notion of quasi-boundedness simplifies H. Miller's proof of D. Sullivan's conjecture on the contractibility of the space of pointed maps from the classifying space of the groupe /2 into a finite complex. |
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