Formal manifold

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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]
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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)
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