The relation between the Baum-Connes Conjecture and the Trace Conjecture

• 成果类型: Article
• 署名作者: Lück, W
• 署名单位: University of Munster
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s002220200215
• 发表日期: 2002
• 页码: 123-152
• 关键词: homology; index

摘要

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 Chem character, which is an isomorphism and lives over the ring Z subset of Lambda(G) subset of 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-o(C-r*(G)) --> R takes values in Lambda(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].