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Surgery on double knots and symmetries

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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Abstract

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
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