EQUIVARIANT PERIODIC CYCLIC HOMOLOGY
EQUIVARIANT PERIODIC CYCLIC HOMOLOGY
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DOI：
10.1017/s1474748007000102
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发表时间：
2004-12
影响因子：
0.9
通讯作者：
Christian Voigt
中科院分区：
文献类型：
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作者：
Christian Voigt
我们定义并研究局部紧群的等变周期循环同调。这可以被视为等变德拉姆上同调的非交换概括。尽管该结构类似于普通循环同调的 Cuntz-Quillen 方法，但等变环境中的一个全新特征是该理论的基本成分不是通常意义上的复形。因此，在等变背景下，只有周期循环理论才能被完全概括地定义。我们的定义恢复了不同作者之前研究的特定案例。我们证明双变等变周期性循环同调是同伦不变的、稳定的并且满足两个变量的切除。此外，我们构建了概括了明显的组合产品的外部产品。最后，我们证明了紧群的循环同调和离散群的对偶结果的 Green-Julg 定理。
We define and study equivariant periodic cyclic homology for locally compact groups. This can be viewed as a non-commutative generalization of equivariant de Rham cohomology. Although the construction resembles the Cuntz–Quillen approach to ordinary cyclic homology, a completely new feature in the equivariant setting is the fact that the basic ingredient in the theory is not a complex in the usual sense. As a consequence, in the equivariant context only the periodic cyclic theory can be defined in complete generality. Our definition recovers particular cases studied previously by various authors. We prove that bivariant equivariant periodic cyclic homology is homotopy invariant, stable and satisfies excision in both variables. Moreover, we construct the exterior product which generalizes the obvious composition product. Finally, we prove a Green–Julg theorem in cyclic homology for compact groups and the dual result for discrete groups.