Invariants de Vassiliev et conjecture de PoincaréVassiliev invariants and the Poincaré conjecture |
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Authors: | Michael Eisermann |
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Institution: | UMPA, École normale supérieure de Lyon, 46, allée d''Italie, 69364 Lyon, France |
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Abstract: | We prove the following result: if Vassiliev invariants distinguish knots in each homotopy sphere, then the Poincaré conjecture is true, in other words every homotopy sphere is homeomorphic to the standard sphere. On the other hand, in every Whitehead manifold there exist knots that cannot be distinguished by Vassiliev invariants. To cite this article: M. Eisermann, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 1005–1010. |
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