| dbo:abstract |
In mathematics, the Farrell–Jones conjecture, named after F. Thomas Farrell and Lowell E. Jones, states that certain assembly maps are isomorphisms. These maps are given as certain homomorphisms. The motivation is the interest in the target of the assembly maps; this may be, for instance, the algebraic K-theory of a group ring or the L-theory of a group ring , where G is some group. The sources of the assembly maps are equivariant homology theory evaluated on the classifying space of G with respect to the family of virtually cyclic subgroups of G. So assuming the Farrell–Jones conjecture is true, it is possible to restrict computations to virtually cyclic subgroups to get information on complicated objects such as or . The Baum–Connes conjecture formulates a similar statement, for the topological K-theory of reduced group -algebras . (en) ボスト予想（en:Bost conjecture）は、1995年にフランスの数学者、ジャン＝ブノワ・ボスが提起した予想で、代数的K-理論と、素数論を統一する予想である。 トーマス・ファレルとローウェルE.ジョーンズにちなんで名付けられたファレル＝ジョーンズの推測（en:Farrell–Jones conjecture）につらなるとされ、これらは特定のアセンブリマップが同型であるとされるが、特定の準同型として与えられた動機は、群環の代数的-K理論とアセンブリマップのターゲットへの関心である。 (ja) |
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yago:WikicatConjectures yago:Abstraction100002137 yago:Cognition100023271 yago:Concept105835747 yago:Content105809192 yago:Hypothesis105888929 yago:Idea105833840 yago:PsychologicalFeature100023100 yago:Speculation105891783 |
| rdfs:comment |
ボスト予想（en:Bost conjecture）は、1995年にフランスの数学者、ジャン＝ブノワ・ボスが提起した予想で、代数的K-理論と、素数論を統一する予想である。 トーマス・ファレルとローウェルE.ジョーンズにちなんで名付けられたファレル＝ジョーンズの推測（en:Farrell–Jones conjecture）につらなるとされ、これらは特定のアセンブリマップが同型であるとされるが、特定の準同型として与えられた動機は、群環の代数的-K理論とアセンブリマップのターゲットへの関心である。 (ja) In mathematics, the Farrell–Jones conjecture, named after F. Thomas Farrell and Lowell E. Jones, states that certain assembly maps are isomorphisms. These maps are given as certain homomorphisms. The motivation is the interest in the target of the assembly maps; this may be, for instance, the algebraic K-theory of a group ring or the L-theory of a group ring , where G is some group. The Baum–Connes conjecture formulates a similar statement, for the topological K-theory of reduced group -algebras . (en) |
| rdfs:label |
Farrell–Jones conjecture (en) ボスト予想 (ja) |
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