Differential Characters for K-theory
Differential Characters for K-theory
复制标题
K 理论的微分特征
DOI：
10.1007/978-3-0348-0257-4_12
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
D. Sullivan
中科院分区：
文献类型：
--
作者：
J. Simons;D. Sullivan
我们描述了一系列结果，这些结果始于七十年代在奇异循环上引入微分特征，其动机是寻找几何不变量或更普遍的具有联系的捆绑。该序列通过使用这些特征的普通微分上同调的 Eilenberg-Steenrod 型唯一性结果，以及使用 Grothendieck 对具有连接的复丛类的构造来构造微分 K 理论。序列的最后一个元素返回完整的圆，并具有微分 K 理论的微分字符定义。微分 K 理论的特征定义中的循环是闭合光滑流形，在其稳定切丛上具有复杂的结构和厄米连接。
We describe a sequence of results that begins with the introduction of differential characters on singular cycles in the seventies motivated by the search for invariants of geometry or more generally bundles with connections. The sequence passes through an Eilenberg-Steenrod type uniqueness result for ordinary differential cohomology using these characters and a construction of a differentialK-theory using Grothendieck’s construction on classes of complex bundles with connection. The last element of the sequence returns full circle with a differential character definition of differentialK-theory. The cycles in this definition of characters for differentialK-theory are closed smooth manifolds provided with complex structures and hermitian connections on their stable tangent bundles.