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- W4386876278 abstract "For a hyperbolic knot in $S^3$, Dehn surgery along slope $r in Q cup {frac10}$ is {em exceptional} if it results in a non-hyperbolic manifold. We say meridional surgery, $r = frac10$, is {em trivial} as it recovers the manifold $S^3$. We provide evidence in support of two conjectures. The first (inspired by a question of Professor Motegi) states that there are boundary slopes $b_1 < b_2$ such that all non-trivial exceptional surgeries occur, as rational numbers, in the interval $[b_1,b_2]$. We say a boundary slope is {em NIT} if it is non-integral or toroidal. Second, when there are non-trivial exceptional surgeries, we conjecture there are NIT boundary slopes $b_1 leq b_2$ so that the exceptional surgeries lie in $[floor{b_1},ceil{b_2}]$. Moreover, if $ceil{b_1} leq floor{b_2}$, the integers in the interval $[ ceil{b_1}, floor{b_2} ]$ are all exceptional surgeries." @default.
- W4386876278 created "2023-09-20" @default.
- W4386876278 creator A5002087391 @default.
- W4386876278 creator A5073524329 @default.
- W4386876278 date "2023-09-18" @default.
- W4386876278 modified "2023-09-27" @default.
- W4386876278 title "Boundary slopes (nearly) bound exceptional slopes" @default.
- W4386876278 doi "https://doi.org/10.48550/arxiv.2309.09918" @default.
- W4386876278 hasPublicationYear "2023" @default.
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