Surgery on double knots and symmetries



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Montesinos Amilibia, José María and Boileau, Michel and González Acuña, Francisco Javier (1987) Surgery on double knots and symmetries. Mathematische Annalen, 276 (2). pp. 323-340. ISSN 0025-5831

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W. Whitten conjectured [Pacific J. Math. 97 (1981), no. 1, 209–216] that no 3-manifold obtained by a nontrivial surgery on a double of a noninvertible knot is a 2-fold branched covering of S3. The authors give counterexamples to this conjecture and determine the exact range of validity of the conjecture. More generally, they consider closed, orientable 3-manifolds obtained by nontrivial Dehn surgery on a double of a non-strongly invertible knot and study the symmetries of such manifolds, i.e. the homeomorphisms of finite order on these manifolds. They show that, except for a finite number of surgeries, these manifolds admit no (nontrivial) symmetry.

Item Type:Article
Uncontrolled Keywords:symmetries of 3-manifolds; Dehn surgeries on a double of a noninvertible knot; 2-fold branched covers of S 3
Subjects:Sciences > Mathematics > Topology
ID Code:17172
Deposited On:22 Nov 2012 10:24
Last Modified:12 Dec 2018 15:13

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