Discrete Hopf Bundle To Contact

We make use of the new approach proposed by Manton[1]to discuss the connections on discrete fibre bundleS¹⁵â†'S⁸.The new approach to lattice gauge fields consists in taking a discrete total space for the bundle,having a finite number of points,the gauge group is a discrete group acting on these points.The fibres are the orbits of this group,and the base space is the quotient of the bundle by the group action.There is therefore one point in the base space for each fibre in the bundle.If the bundle is twisted.the gauge fields are topologically non-trivial automatically.A fundamental consequence of the fact that the Hopf bundles S¹⁵â†'S⁸ are twisted is that there is no flat connection on them.