标题： 超连接与非交换几何 显示英文标题

标题： Super-connections and non-commutative geometry

摘要： 我们证明了使用超连接计算指标的陈特征的Quillen形式主义可以扩展到具有函数演算的任意算子。 因此，我们去除了算子在同伦意义下谱中存在间隙的条件。 这是通过微分分次代数和非交换微分形式证明的。 我们的结果还给出了一个关于使用超连接定义的差分丛的陈特征与经典定义相一致的新证明。 显示英文摘要

摘要： We show that Quillen's formalism for computing the Chern character of the index using superconnections extends to arbitrary operators with functional calculus. We thus remove the condition that the operators have, up to homotopy, a gap in the spectrum. This is proved using differential graded algebras and non-commutative differential forms. Our results also give a new proof of the coincidence of the Chern character of a difference bundle defined using super-connections with the classical definition.