Coarse topology, enlargeability, and essentialness
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 41 (2008) no. 3, p. 473-495

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.

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.

DOI : https://doi.org/10.24033/asens.2073
Classification:  53C23,  55N99,  19K35,  19K56
@article{ASENS_2008_4_41_3_473_0,
     author = {Hanke, Bernhard and Kotschick, Dieter and Roe, John and Schick, Thomas},
     title = {Coarse topology, enlargeability, and essentialness},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 41},
     number = {3},
     year = {2008},
     pages = {473-495},
     doi = {10.24033/asens.2073},
     zbl = {1169.53032},
     mrnumber = {2482205},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2008_4_41_3_473_0}
}
Hanke, Bernhard; Kotschick, Dieter; Roe, John; Schick, Thomas. Coarse topology, enlargeability, and essentialness. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 41 (2008) no. 3, pp. 473-495. doi : 10.24033/asens.2073. http://www.numdam.org/item/ASENS_2008_4_41_3_473_0/

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