Characteristic subsurfaces and Dehn filling

Boyer, Steven; Culler, Marc; Shalen, Peter B. et Zhang, Xingru (2005). « Characteristic subsurfaces and Dehn filling ». Transactions of the American Mathematical Society, 357(06), pp. 2389-2445.

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Résumé

Let M be a simple knot manifold. Using the characteristic submanifold theory and the combinatorics of graphs in surfaces, we develop a method for bounding the distance between the boundary slope of an essential surface in M which is not a fiber or a semi-fiber, and the boundary slope of a certain type of singular surface. Applications include bounds on the distances between exceptional Dehn surgery slopes. It is shown that if the fundamental group of M(α) has no non-abelian free subgroup, and if M(β) is a reducible manifold which is not homeomorphic to S 1 × S 2 or P 3 # P 3, then Δ(α, β) ≤ 5. Under the same condition on M(β), it is shown that if M (α) is Seifert fibered, then Δ(α, β) ≤ 6. Moreover, in the latter situation, character variety techniques are used to characterize the topological types of M(α) and M(β) in case the bound of 6 is attained.

Type: Article de revue scientifique
Mots-clés ou Sujets: dehn filling, knot manifold, combinatorics
Unité d'appartenance: Faculté des sciences > Département de mathématiques
Déposé par: Steven P. Boyer
Date de dépôt: 26 avr. 2016 19:24
Dernière modification: 19 mai 2016 17:57
Adresse URL : http://www.archipel.uqam.ca/id/eprint/8317

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