Coarse topology, enlargeability, and essentialness
[Topologie à grande échelle, agrandissabilité et non-annulation en homologie]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 41 (2008) no. 3, pp. 473-495.

En utilisant des méthodes de topologie à grande échelle, on prouve que les classes fondamentales des variétés agrandissables ne s’annulent pas, ni dans l’homologie rationnelle de leurs groupes fondamentaux, ni dans la K-théorie des C * -algèbres réduites correspondantes. Nos résultats ne dépendent pas de la conjecture de Baum-Connes, et confirment de façon indépendante certaines conséquences de cette conjecture.

Using methods from coarse topology we show that fundamental classes of closed enlargeable manifolds map non-trivially both to the rational homology of their fundamental groups and to the K-theory of the corresponding reduced C * -algebras. Our proofs do not depend on the Baum-Connes conjecture and provide independent confirmation for specific predictions derived from this conjecture.

DOI : 10.24033/asens.2073
Classification : 53C23, 55N99, 19K35, 19K56
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Hanke, Bernhard; Kotschick, Dieter; Roe, John; Schick, Thomas. Coarse topology, enlargeability, and essentialness. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 41 (2008) no. 3, pp. 473-495. doi : 10.24033/asens.2073. http://www.numdam.org/articles/10.24033/asens.2073/

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