Formal manifold

In geometry and topology, a formal manifold can mean one of a number of related concepts:

• In the sense of Dennis Sullivan, a formal manifold is one whose real homotopy type is a formal consequence of its real cohomology ring; algebro-topologically this means that all Massey products vanish.^[1]
• A stronger notion is a geometrically formal manifold, which is the condition that all wedge products of harmonic forms are harmonic.^[2]

References

1. ^ Manifolds, Proc. Int. Conf., Tokyo, 1973 (1975; ; Zbl 0319.58005)
2. ^ Kotschick, D. On products of harmonic forms. (English) Duke Math. J. 107, No.3, 521–531 (2001)