Title: Combinatorial formulas for the first rational Pontryagin class and applications
Speaker: Denis Gorodkov - Steklov Mathematical Institute
Abstract: The combinatorial computation of rational Pontryagin classes of a manifold given its triangulation is a classical problem of algebraic topology arising in the 1970’s. Works on the subject include the praised Gabrielov-Gelfand-Losik 1975 article, several articles by Gelfand and MacPherson and many more. In 2004 Prof. Alexander Gaifullin explicitly described the set of all local formulas for the first Pontryagin class in a computable way. We will give a general overview of the subject, present some recent results and demonstrate a nice application proving that a special simplicial complex is the vertex-minimal triangulation of the quaternionic projective plane.
