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• W3105817808 abstract "In this paper we investigate the question of when different surgeries on a knot can produce identical manifolds. We show that given a knot in a homology sphere, unless the knot is quite special, there is a bound on the number of slopes that can produce a fixed manifold that depends only on this fixed manifold and the homology sphere the knot is in. By finding a different bound on the number of slopes, we show that non-null-homologous knots in certain homology $mathbb{R}P^3$'s are determined by their complements. We also prove the surgery characterisation of the unknot for null-homologous knots in $L$-spaces. This leads to showing that all knots in some lens spaces are determined by their complements. Finally, we establish that knots of genus greater than $1$ in the Brieskorn sphere $Sigma(2,3,7)$ are also determined by their complements." @default.
• W3105817808 created "2020-11-23" @default.
• W3105817808 creator A5048340306 @default.
• W3105817808 date "2018-01-10" @default.
• W3105817808 modified "2023-09-26" @default.
• W3105817808 title "Heegaard Floer homology and knots determined by their complements" @default.
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• W3105817808 doi "https://doi.org/10.2140/agt.2018.18.69" @default.
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