Bounds on exceptional Dehn filling

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Ian Agol This is my paper · ORCID

classification math.GT

keywords dehnboundscomplementexceptionalfillingfillingsfundamentalgroup

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We show that for a hyperbolic knot complement, all but at most 12 Dehn fillings are irreducible with infinite word-hyperbolic fundamental group.

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Expansion joints in hyperbolic manifolds
math.GT 2025-11 conditional novelty 7.0 of 10

Cone-deforming an ideal arc through 'expansion joints' interpolates between stacked Borromean ring complements and lantern manifolds, and yields cone deformations of highly twisted 2-bridge unknotting tunnels.