论文标题
离散组和几乎扁平K理论的母系稳定性的障碍
Obstructions to matricial stability of discrete groups and almost flat K-theory
论文作者
论文摘要
如果有限维数近似统一表示G在点 - 拓扑中的真实表示形式，则具有离散的可计数G组在术中是稳定的。对于大类G组，我们表明母系稳定性意味着在所有非零尺寸中G的理性同胞的消失。我们重新审视一种构建BG几乎平坦的K理论类别的方法，该类别涉及G的双组装图和准分子性的特性。存在几乎平坦的BG的BG的存在，这些类别不是平坦的，这代表了由于近似单骨术的连续性而导致G的术语G的障碍物。
A discrete countable group G is matricially stable if the finite dimensional approximate unitary representations of G are perturbable to genuine representations in the point-norm topology. For large classes of groups G, we show that matricial stability implies the vanishing of the rational cohomology of G in all nonzero even dimensions. We revisit a method of constructing almost flat K-theory classes of BG which involves the dual assembly map and quasidiagonality properties of G. The existence of almost flat K-theory classes of BG which are not flat represents an obstruction to matricial stability of G due to continuity properties of the approximate monodromy correspondence.
