A combinatorial formula for the first Pontryagin class in terms of combinatorial curvature redistribution

The problem of finding explicit formulae for the rational Pontryagin classes of a combinatorial manifold is classical in algebraic topology. In the case of the first Pontryagin class Prof. Alexander Gaifullin devised a computable explicit algorithm in 2004. More precisely, he described the set of all local formulae for the first Pontryagin class of a combinatorial manifold, and, therefore, it is natural to look for a canonical precise formula from this set. We will demonstrate such a choice based on the redistribution of combinatorial curvature under bistellar flips of two-dimensional spheres. The talk is based on a joint work with Prof. Alexander Gaifullin.