在数学中，纤维丛上一个联络是一个定义丛上平行移动的装置；即将邻近点连接或等价的一种方法。如果纤维丛是矢量丛，则平行移动的概念要求线性。这样的联络等价于一个共变导数，共变导数是一个能对截面关于底流形的切方向求微分的算子。联络在这个意义下，对任意矢量丛，推广了光滑流形切丛的线性联络概念，经常叫做线性联络。

矢量丛上的联络也经常称为科斯居尔联络，以让-路易·科斯居尔命名，他给出了描述这个联络的一个代数框架 （Koszul 1950）。

In mathematics, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. If the fiber bundle is a vector bundle, then the notion of parallel transport must be linear. Such a connection is equivalently specified by a covariant derivative, which is an operator that can differentiate sections of that bundle along tangent directions in the base manifold. Connections in this sense generalize, to arbitrary vector bundles, the concept of a linear connection on the tangent bundle of a smooth manifold, and are sometimes known as linear connections. Nonlinear connections are connections that are not necessarily linear in this sense.