ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: nnot given Vaccaro, Michelangelo, Roma, Italy Unicity of the topological type of the simply connected manifolds Three independant proofs of the theorem in the title, as conjectured by Poincaré. The first proof splits the 3-manifold in blocks by parallel sections, followed by soldering of them in a 3-sphere. The second proof utilities a Heegard splitting of the 3-manifold, a line on the dividing surface with linking numbers zero regarding one handlebody, a particular 3-disc bounded by it, and with this deduces a Heegard splitting inferior genus. The third proof determines a particular simplicial map of S^{3} onto M^{3} and smoothes it in a homeomorphism by iterate smoothing the prototypes of the dual cells of the triangulation. It utilises the Fox characterization of the 3-spherical parts. The second and the third proof utilise the Dehn Lemma.