AbstractThe classical differential calculus of a higher order is provided by the graded algebra of differential forms on a smooth manifold with the operation of exterior differentiation. Our interest to this notion was motivated by a desire to develop a calculus of differential forms on discrete objects. As a rule, the role of discrete objects is played by discrete sets with additional relation...
AbstractThe classification of manifolds in various categories is a classical problem in topology. It has been widely investigated by applying techniques from geometric topology in the last century. However, the known results tell us very little information about the homotopy of manifolds. In the last ten years, there have been attempts to study the homotopy properties of manifolds by using tech...
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