有限和扭转KK-理论
Finite and torsion KK-theories
摘要：
本文在Arlettaz-H.Inassaridze的有限代数K理论的基础上发展了C ~*-代数的有限KKG理论。将有限代数K理论中关于元阶的Browder-Karoubi-Lambre定理推广到有限KKG理论。定义了一个新的双变理论，称为挠KK-理论，作为有限KK-理论的直接极限。这样的双变K-理论具有几乎所有的KKG-理论性质，并且有一个长的正合序列将KK-理论、有理双变K-理论和挠KK-理论联系起来。对于给定的可分GC*-代数范畴上的同调论，引入并研究了有限同调理论、有理同调理论和挠同调论。特别是，我们制定有限的，扭转和合理的版本鲍姆-康纳斯猜想。后者相当于对所有素数q的鲍姆-康纳斯猜想的有理和q-有限类似物的研究。
英文摘要：
We develop a finite KKG-theory of C*-algebras following Arlettaz- H.Inassaridze's approach to finite algebraic K-theory. The Browder- Karoubi-Lambre's theorem on the orders of the elements for finite algebraic K-theory is extended to finite KKG-theory. A new bivariant theory, called torsion KK-theory is defined as the direct limit of finite KK-theories. Such bivariant K-theory has almost all KKG-theory properties and one has a long exact sequence relating KK-theory, rational bivariant K-theory and torsion KK-theory. For a given homology theory on the category of separable GC*-algebras finite, rational and torsion homology theories are introduced and investigated. In particular, we formulate finite, torsion and rational versions of Baum-Connes Conjecture. The later is equivalent to the investigation of rational and q-finite analogues for Baum-Connes Conjecture for all prime q.
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