Exceptional surgeries on $(-2,p,p)$-pretzel knots

Details Exceptional surgeries on $(-2,p,p)$-pretzel knots Exceptional surgeries on $(-2,p,p)$-pretzel knots

2011-02-06

arxiv.org/abs/1102.1118v1

Mathematics

Geometric Topology

13 pages, 15 figures

Scientific paper

We give a complete description of exceptional surgeries on pretzel knots of type $(-2, p, p)$ with $p \ge 5$. It is known that such a knot admits a unique toroidal surgery yielding a toroidal manifold with a unique incompressible torus. By cutting along the torus, we obtain two connected components, one of which is a twisted $I$-bundle over the Klein bottle. We show that the other is homeomorphic to the one obtained by certain Dehn filling on the magic manifold. On the other hand, we show that all such pretzel knots admit no Seifert fibered surgeries.

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