The conjecture is formulated as follows: If X is usually a projective manifold, any course of rational homology of variety (p, p) may be represented by complicated submanifolds with the advanced dimension p. The formulation is proposed being an extension of Thom’s aforementioned consequence, where any course of rational homology of dimension k can be represented by a submanifold (a true a person, which can be comprehended when It's not specified) of dimension k.

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They bring about unique traits up to date with The latest advancements as well as important Fields medals are awarded at them. Hodge was a plenary lecturer, and in his speech he offered the modern – at enough time – principle of harmonic varieties for the study from the topology of complicated differentiable manifolds, identified currently as being the Hodge principle. He also proposed extending a pure results of the representativeness of homology lessons with submanifolds in differentiable manifolds to the situation of advanced manifolds.

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