超连接的迭代积分
Iterated integrals of superconnections
摘要：
从光滑流形M上的分次向量丛上的Z-分次超连通出发，证明了在M中光滑单形上的这种超连通的Chen迭代积分给出A-无穷函子的充要条件是超连通是平坦的.如果分次丛是平凡的，这给出一个扭曲上链。K. T.陈用类似的方法。本文的目的是从头开始解释这一点开始的定义和基本性质的连接和结束的论述陈的“形式连接”和简要讨论这是如何与更高的Reidemeister扭转。
英文摘要：
Starting with a Z-graded superconnection on a graded vector bundle over a smooth manifold M, we show how Chen's iterated integration of such a superconnection over smooth simplices in M gives an A-infinity functor if and only if the superconnection is flat. If the graded bundle is trivial, this gives a twisting cochain. Very similar results were obtained by K.T. Chen using similar methods. This paper is intended to explain this from scratch beginning with the definition and basic properties of a connection and ending with an exposition of Chen's "formal connections" and a brief discussion of how this is related to higher Reidemeister torsion.
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