霍普夫代数、循环上同调与横指标理论
Hopf algebras, cyclic cohomology and the transverse index theory
摘要：
我们提出了解决非交换几何的一个长期存在的内部问题，即计算任意叶理上的横截椭圆算子的指数。新的和关键的成分是一个特定的霍普夫代数相关的横向标架丛。它的循环上同调的定义和证明是典型同构的Gelfand-Fuks上同调。
英文摘要：
We present the solution of a longstanding internal problem of noncommutative geometry, namely the computation of the index of a transversally elliptic operator on an arbitrary foliation. The new and crucial ingredient is a certain Hopf algebra associated to the transverse frame bundle. Its cyclic cohomology is defined and shown to be canonically isomorphic to the Gelfand-Fuks cohomology.
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