The Geography of Non-Formal Manifolds

Abstract

We show that there exist non-formal compact oriented manifolds of dimension n and with first Betti number b 1 = b ≥ 0 if and only if n ≥ 3 and b ≥ 2, or n ≥ (7 − 2b) and 0 ≤ b ≤ 2. Moreover, we present explicit examples for each one of these cases.