Coarse topology, enlargeability, and essentialness

Bernhard Hanke; Dieter Kotschick; John Roe; Thomas Schick

Annales scientifiques de l'École Normale Supérieure (2008)

  • Volume: 41, Issue: 3, page 473-495
  • ISSN: 0012-9593

Abstract

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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.

How to cite

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Hanke, Bernhard, et al. "Coarse topology, enlargeability, and essentialness." Annales scientifiques de l'École Normale Supérieure 41.3 (2008): 473-495. <http://eudml.org/doc/272174>.

@article{Hanke2008,
abstract = {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.},
author = {Hanke, Bernhard, Kotschick, Dieter, Roe, John, Schick, Thomas},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {enlargeable manifold; universally enlargeable manifold; essential manifold; macroscopically large manifold; coarse homology; Baum-Connes assembly map; -theory enlargeability; scalar curvature},
language = {eng},
number = {3},
pages = {473-495},
publisher = {Société mathématique de France},
title = {Coarse topology, enlargeability, and essentialness},
url = {http://eudml.org/doc/272174},
volume = {41},
year = {2008},
}

TY - JOUR
AU - Hanke, Bernhard
AU - Kotschick, Dieter
AU - Roe, John
AU - Schick, Thomas
TI - Coarse topology, enlargeability, and essentialness
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2008
PB - Société mathématique de France
VL - 41
IS - 3
SP - 473
EP - 495
AB - 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.
LA - eng
KW - enlargeable manifold; universally enlargeable manifold; essential manifold; macroscopically large manifold; coarse homology; Baum-Connes assembly map; -theory enlargeability; scalar curvature
UR - http://eudml.org/doc/272174
ER -

References

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