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- W3209806543 startingPage "2649" @default.
- W3209806543 abstract "Work of Ni and Zhang has shown that for the torus knot $T_{r,s}$ with $r>s>1$ every surgery slope $p/q geq frac{30}{67}(r^2-1)(s^2-1)$ is a characterizing slope. In this paper, we show that this can be lowered to a bound which is linear in $rs$, namely, $p/qgeq frac{43}{4}(rs-r-s)$. The main technical ingredient in this improvement is to show that if $Y$ is an $L$-space bounding a sharp 4-manifold which is obtained by $p/q$-surgery on a knot $K$ in $S^3$ and $p/q$ exceeds $4g(K)+4$, then the Alexander polynomial of $K$ is uniquely determined by $Y$ and $p/q$. We also show that if $p/q$-surgery on $K$ bounds a sharp 4-manifold, then $S^3_{p'/q'}(K)$ bounds a sharp 4-manifold for all $p'/q'geq p/q$." @default.
- W3209806543 created "2021-11-08" @default.
- W3209806543 creator A5081262622 @default.
- W3209806543 date "2021-10-31" @default.
- W3209806543 modified "2023-10-01" @default.
- W3209806543 title "Surgeries, sharp 4–manifolds and the Alexander polynomial" @default.
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- W3209806543 doi "https://doi.org/10.2140/agt.2021.21.2649" @default.
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