The relation between the Baum-Connes Conjecture and the Trace Conjecture |
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Authors: | Wolfgang Lück |
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Institution: | 1.Fachbereich Mathematik und Informatik, Westf?lische Wilhelms-Universit?t Münster, Einsteinstr. 62, 48149 Münster, Germany (e-mail: lueck@math.uni-muenster.de; http://www.math.uni-muenster.de/u/lueck),Germany |
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Abstract: | We prove a version of the L
2-index Theorem of Atiyah, which uses the universal center-valued trace instead of the standard trace. We construct for G-equivariant K-homology an equivariant Chern character, which is an isomorphism and lives over the ring ℤ⊂λ
G
⊂ℚ obtained from the integers by inverting the orders of all finite subgroups of G. We use these two results to show that the Baum-Connes Conjecture implies the modified Trace Conjecture, which says that
the image of the standard trace K
0(C
*
r
(G))→ℝ takes values in λ
G
. The original Trace Conjecture predicted that its image lies in the additive subgroup of ℝ generated by the inverses of all
the orders of the finite subgroups of G, and has been disproved by Roy 15].
Oblatum 10-IV-2001 & 18-X-2001?Published online: 15 April 2002 |
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Keywords: | Mathematical Subject Classification (2000): 19L47 19K56 55N91 |
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