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 in particular 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
Sullivan, Dennis (1975). "Differential forms and the topology of manifolds". Manifolds—Tokyo 1973 (Proc. Internat. Conf., Tokyo, 1973). Tokyo: University of Tokyo Press. pp. 37–49. MR 0370611. Zbl 0319.58005.
Kotschick, Dieter (2001). "On products of harmonic forms". Duke Mathematical Journal. 107 (3): 521–531. arXiv:math/0004009. doi:10.1215/S0012-7094-01-10734-5. MR 1828300.
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