%0 Journal Article
%A Montesinos Amilibia, José María
%A Boileau, Michel
%A González Acuña, Francisco Javier
%T Surgery on double knots and symmetries
%D 1987
%@ 0025-5831
%U https://hdl.handle.net/20.500.14352/57722
%X 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.
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