  By p(|K|) denote the characteristic class of a combinatorial manifold K given
by the polynomial p in Pontrjagin classes of K. We prove that for any
polynomial p there exists a function taking each combinatorial manifold K to a
rational simplicial cycle z(K) such that: (1) the Poincare dual of z(K)
represents the cohomology class p(|K|); (2) a coefficient of each simplex in
the cycle z(K) is determined only by the combinatorial type of the link of this
simplex. We also prove that if a function z satisfies the condition (2), then
this function automatically satisfies the condition (1) for some polynomial p.
We describe explicitly all such functions z for the first Pontrjagin class. We
obtain estimates for denominators of coefficients of simplices in the cycles
z(K).
