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Let π : L → K be a map of simplicial complexes, whose geometric realization is homeomorphic to a locally trivial fiber bundle. There is a long-standing problem to express the characteristic classes of this bundle in terms of the combinatorics of this map. In my talk I will describe the solution of this problem in the simplest case (when the fiber is equal to the circle S1) and give few insights into the possible solutions of the general case.