Geodesic
Essential curves in handlebodies and topological contractions
Grines, Viatcheslav1 ; Laudenbach, François2
1 N. Novgorod State University, Gagarina 23, N. Novgorod, 603950 Russia
2 Laboratoire de mathématiques Jean Leray, UMR 6629 du CNRS, Faculté des Sciences et Techniques, Université de Nantes, 2, rue de la Houssinière, F-44322 Nantes cedex 3, France
Geometry & topology, Tome 12 (2008) no. 2, pp. 981-985.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

If X is a compact set, a topological contraction is a self-embedding f such that the intersection of the successive images fk(X), k > 0, consists of one point. In dimension 3, we prove that there are smooth topological contractions of the handlebodies of genus ≥ 2 whose image is essential.

DOI : 10.2140/gt.2008.12.981
Keywords: Heegaard splitting, compression disk, North-South diffeomorphism

Grines, Viatcheslav 1 ; Laudenbach, François 2

1 N. Novgorod State University, Gagarina 23, N. Novgorod, 603950 Russia
2 Laboratoire de mathématiques Jean Leray, UMR 6629 du CNRS, Faculté des Sciences et Techniques, Université de Nantes, 2, rue de la Houssinière, F-44322 Nantes cedex 3, France 
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Grines, Viatcheslav; Laudenbach, François. Essential curves in handlebodies and topological contractions. Geometry & topology, Tome 12 (2008) no. 2, pp. 981-985. doi : 10.2140/gt.2008.12.981. http://geodesic.mathdoc.fr/articles/10.2140/gt.2008.12.981/

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[3] F Waldhausen, Heegaard-Zerlegungen der $3$–Sphäre, Topology 7 (1968) 195

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