Gelʹfand, I. M. and MacPherson, R. D. "A combinatorial formula for the Pontrjagin classes" Bull. Amer. Math. Soc. (N.S.) 26 (1992), no. 2, 304–309. 


In the above paper the authors claimed a construction of combinatorial formula for the Pontrjagin classes. According to mathscinet review: MR1129313, it seems the construction is not really local. So the existence of such formula is still open?


Also for first Pontrjagin class, do I understand correctly that "Gabrièlov, A. M.; Gelʹfand, I. M.; Losik, M. V. A local combinatorial formula for the first Pontrjagin class" is a well know result? If so is there any English paper gave detailed constructions?



Does combinatorial formula for the Pontrjagin classes exist?
I believe there is a formula like the one you seek together with a good survey of the previous literature in the paper "Local formulae for combinatorial Pontrjagin classes" by Gaifullin, available [here](http://arxiv.org/abs/math/0407035).


