ALGEBRAIC CONNECTIONS ON PARALLEL UNIVERSES

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Abstract
For any manifold M we introduce a ℤ-graded differential algebra Ξ, which, in particular, is a bimodule over the associative algebra C(M⋃M). We then introduce the corresponding covariant differentials and show how this construction can be interpreted in terms of Yang-Mills and Higgs fields. This is a particular example of noncommutative geometry. It differs from the prescription of Connes in the following way: the definition of Ξ does not rely on a given Dirac-Yukawa operator acting on a space of spinors.
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