# Massey Triple Products

# 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, $f : M \rightarrow N$ , 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 $$ between the image of this triple product in dimension $r$ with the image in dimension $n+|x_1|+|x_2|-1-r$.