K– and L–theory of the semi-direct product of the discrete 3–dimensional Heisenberg group by ℤ∕4
K– and L–theory of the semi-direct product of the discrete 3–dimensional Heisenberg group by ℤ∕4
复制标题
离散 3 维海森堡群与 ℤ∕4 的半直积的 K– 和 L– 理论
DOI：
10.2140/gt.2005.9.1639
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发表时间：
2004
影响因子：
2
通讯作者：
W. Lueck
中科院分区：
文献类型：
--
作者：
W. Lueck
计算了三维离散Heisenberg群的Z/4半直积的群同调、约化C*-代数的拓扑K-理论、群环的代数K-理论和代数L-理论.这些计算将从对某类群G的更一般的处理中得出，这类群G作为无挠群K被满足某些假设的群Q的扩张1→ K → G → Q → 1出现。关键成分是鲍姆-康纳斯和法雷尔-琼斯猜想和方法从等变代数拓扑。
We compute the group homology, the topological K-theory of the reduced C*-algebra, the algebraic K-theory and the algebraic L-theory of the group ring of the semi-direct product of the three-dimensional discrete Heisenberg group by Z/4. These computations will follow from the more general treatment of a certain class of groups G which occur as extensions 1→ K → G → Q → 1 of a torsionfree group K by a group Q which satisfies certain assumptions. The key ingredients are the Baum-Connes and Farrell-Jones Conjectures and methods from equivariant algebraic topology.