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, a manifold on which all wedge products of harmonic forms are harmonic.[2]

References

  1. 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. 
  2. Kotschick, Dieter (2001). "On products of harmonic forms". Duke Mathematical Journal 107 (3): 521–531. doi:10.1215/S0012-7094-01-10734-5.