Abstract: A non-zero degree map between closed orientable
manifolds induces an injection of rational cohomology algebras. The
key property used in this quick argument, namely Poincare duality, in
fact sees more than just the ring structure: as shown by L. Taylor, a
non-trivial triple Massey product (an operation taking in three
rational cohomology classes) is pulled back to a non-trivial triple
Massey product under a non-zero degree map. I will discuss a recent
result with J. Stelzig and L. Zoller showing that formality is
preserved under non-zero degree maps. Namely, if the domain manifold
is formal, then so is the target. A formal manifold is one whose
differential graded algebra of forms is determined by the cohomology
algebra alone; on such a manifold, all triple and higher-order Massey
products are trivial. Some geometric applications, old and new, will
be given.