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DUALIZING THE COARSE ASSEMBLY MAP

Published online by Cambridge University Press:  07 December 2005

Heath Emerson  and
Ralf Meyer
Heath Emerson
Affiliation:
Mathematics and Statistics, University of Victoria, PO Box 3045 STN CSC, Victoria, BC V8W 3P4, Canada (hemerson@math.uvic.ca)
Ralf Meyer
Affiliation:
Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstraβe 3–5, 37073 Göttingen, Germany (rameyer@uni-math.gwdg.de)
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Abstract

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We formulate and study a new coarse (co-)assembly map. It involves a modification of the Higson corona construction and produces a map dual in an appropriate sense to the standard coarse assembly map. The new assembly map is shown to be an isomorphism in many cases. For the underlying metric space of a group, the coarse co-assembly map is closely related to the existence of a dual Dirac morphism and thus to the Dirac dual Dirac method of attacking the Novikov conjecture.

Keywords

Novikov conjecturecoarse geometryHigson compactificationcoarse Baum–Connes conjecturescalable spacePrimary 19K3546L80
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 5 , Issue 2 , April 2006 , pp. 161 - 186
Copyright
2006 Cambridge University Press