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Simplifying 3-manifolds in 4
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 24 (2015) no. 5, pp. 1079-1101.

We show that a smooth embedding of a closed 3-manifold in S 3 × can be isotoped so that every generic level divides S 3 ×t into two handlebodies (i.e., is Heegaard) provided the original embedding has a unique local maximum with respect to the coordinate. This allows uniqueness of embeddings to be studied via the mapping class group of surfaces and the Schoenflies conjecture is considered in this light. We also give a necessary and sufficient condition that a 3-manifold connected summed with arbitrarily many copies of S 1 ×S 2 embeds in 4 .

Nous montrons qu’un plongement lisse d’une 3-variété fermée dans S 3 × peut être isotopé sorte que chaque niveau générique divise S 3 ×t en deux corps d’anses (i.e., est Heegaard) à condition que le plongement original a un maximum local unique par rapport à la coordonnée . Ceci permet d’étudier l’unicité des plongements en utilisant le groupe de classe de difféotopies des surfaces et la conjecture de Schoenflies est considérée dans cette optique. Nous donnons aussi une condition nécessaire et suffisante pour que la somme connexe d’une 3-variété et d’un nombre arbitraire de copies de S 1 ×S 2 se plonge dans 4 .

Published online:
DOI: 10.5802/afst.1476
@article{AFST_2015_6_24_5_1079_0,
     author = {Ian Agol and Michael Freedman},
     title = {Simplifying $3$-manifolds in ${\mathbb{R}}^4$},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {1079--1101},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 24},
     number = {5},
     year = {2015},
     doi = {10.5802/afst.1476},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1476/}
}
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Ian Agol; Michael Freedman. Simplifying $3$-manifolds in ${\mathbb{R}}^4$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 24 (2015) no. 5, pp. 1079-1101. doi : 10.5802/afst.1476. https://afst.centre-mersenne.org/articles/10.5802/afst.1476/

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