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Surgery on double knots and symmetries. (English) Zbl 0624.57013
This paper studies symmetries (i.e. homeomorphisms of finite order) of 3- manifolds obtained by Dehn surgeries on a double of a noninvertible knot, and shows that these manifolds admit no nontrivial symmetry except for a finite number of surgeries. Moreover, it determines when these manifolds are 2-fold branched covers of \(S^ 3\); this gives the exact range of validity of the conjecture of Whitten that “no manifold obtained by a nontrivial surgery on a double of a noninvertible knot is a 2-fold branched covering of \(S^ 3\)”.
Reviewer: M.Sakuma

MSC:
57N10 Topology of general \(3\)-manifolds (MSC2010)
57M25 Knots and links in the \(3\)-sphere (MSC2010)
57M12 Low-dimensional topology of special (e.g., branched) coverings
57R50 Differential topological aspects of diffeomorphisms
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