Contact structures and reducible surgeries
2015 ◽
Vol 152
(1)
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pp. 152-186
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Keyword(s):
Genus 2
◽
We apply results from both contact topology and exceptional surgery theory to study when Legendrian surgery on a knot yields a reducible manifold. As an application, we show that a reducible surgery on a non-cabled positive knot of genus$g$must have slope$2g-1$, leading to a proof of the cabling conjecture for positive knots of genus 2. Our techniques also produce bounds on the maximum Thurston–Bennequin numbers of cables.
2010 ◽
Vol 146
(4)
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pp. 1096-1112
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Keyword(s):
2018 ◽
Vol 27
(11)
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pp. 1843008
Keyword(s):
2018 ◽
Vol 482
(4)
◽
pp. 385-388
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Keyword(s):
Keyword(s):