On local combinatorial formulae for Pontryagin classes

On local combinatorial formulae for Pontryagin classes

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Alexander Gaifullin, Moscow State University, Steklov Institute of Mathematics
Fine Hall 314

The talk will be devoted to the problem of combinatorial computation of the rational Pontryagin classes of a triangulated manifold. This problem goes back to the famous work by A. M. Gabrielov, I. M. Gelfand, and M. V. Losik (1975). Since then several different approaches to combinatorial computation of the Pontryagin classes have been suggested. However, these approaches require a combinatorial manifold to be endowed with some additional structure such as smoothing or certain its discrete analogue. We suggest a new approach based on the concept of a universal local formula. This approach allows us to construct an explicit combinatorial formula for the first Pontryagin class that can be applied to any combinatorial manifold without any additional structure.