3/22/2011

Larry Taylor
IAS

Massey Triple Products

A technique will be discussed to control the indeterminacy in cohomology Massey triple products. A variety of non-vanishing and vanishing results for Massey triple products are proved using this technique. Here are three examples. • Many authors have noticed that non-trivial triple products in a submanifold produce non-trivial triple products in the blowup along the submanifold. • Given a map of closed, compact manifolds of the same dimension, f : M → N , then non- trivial triple products with field coefficients in N pull back to non-trivial triple products in M provided the degree of the map is non-zero in the field. • Given two classes x_1 and x_2 in an n-manifold, there is a dual pairing for triple products<x_1,?,x_2> between the image of this triple product in dimension r with the image in dimension n+|x_1|+|x_2|-1-r.