The Baum-Connes conjecture, noncommutative Poincaré duality, and the boundary of the free group

Heath Emerson

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-21

Abstract:

For every hyperbolic group Γ with Gromov boundary ∂ Γ , one can form the cross product C ∗ -algebra C ( ∂ Γ ) ⋊ Γ . For each such algebra, we construct a canonical K -homology class. This class induces a Poincaré duality map K ∗ ( C ( ∂ Γ ) ⋊ Γ ) → K ∗ + 1 ( C ( ∂ Γ ) ⋊ Γ ) . We show that this map is an isomorphism in the case of Γ = 𝔽 2 , the free group on two generators. We point out a direct connection between our constructions and the Baum-Connes conjecture and eventually use the latter to deduce our result.

Date: 2003
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2003/629618.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2003/629618.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:629618

DOI: 10.1155/S0161171203209169

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().