主非交换环面丛
Principal noncommutative torus bundles
摘要：
本文研究了C*-代数的连续丛，它们是主环面丛的非交换类似物。我们表明，所有这样的束，虽然在一般情况下是非常远离局部平凡的束，至少是局部平凡的相对于一个合适的束版本的双变K-理论（表示RKK-理论）由于卡斯帕罗夫。利用Echterhoff和Williams的早期结果，我们将给出直到等变Morita等价的主非交换环面丛的完全分类。然后，我们研究这些丛拓扑纤维化（忘记群作用），并给出充要条件的任何非交换主环面丛RKK-等价于一个交换。作为我们方法的一个应用，我们还将给出Mathai和Rosenberg所研究的具有H-通量的具有“经典”T-通量的主环面丛的K-理论特征。
英文摘要：
In this paper we study continuous bundles of C*-algebras which are non-commutative analogues of principal torus bundles. We show that all such bundles, although in general being very far away from being locally trivial bundles, are at least locally trivial with respect to a suitable bundle version of bivariant K-theory (denoted RKK-theory) due to Kasparov. Using earlier results of Echterhoff and Williams, we shall give a complete classification of principal non-commutative torus bundles up to equivariant Morita equivalence. We then study these bundles as topological fibrations (forgetting the group action) and give necessary and sufficient conditions for any non-commutative principal torus bundle being RKK-equivalent to a commutative one. As an application of our methods we shall also give a K-theoretic characterization of those principal torus-bundles with H-flux, as studied by Mathai and Rosenberg which possess "classical" T-duals.
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