Hyperbolic knots with three toroidal Dehn surgeries
Masakazu Teragaito

TL;DR
This paper demonstrates that infinitely many hyperbolic knots can have exactly three toroidal Dehn surgeries, supporting the conjecture that such knots admit at most three such surgeries, with these surgeries occurring at consecutive integers.
Contribution
The authors construct infinitely many hyperbolic knots with exactly three toroidal Dehn surgeries at consecutive integers, providing evidence for the conjectured maximum.
Findings
Existence of infinitely many hyperbolic knots with three toroidal surgeries
Surgeries occur at consecutive integer slopes
Supports the conjecture on the maximum number of such surgeries
Abstract
It is conjectured that a hyperbolic knot admits at most three Dehn surgeries which yield closed three manifolds containing incompressible tori. We show that there exist infinitely many hyperbolic knots which attain the conjectural maximum number. Interestingly, those surgeries correspond to consecutive integers.
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Taxonomy
TopicsGeometric and Algebraic Topology · Connective tissue disorders research · semigroups and automata theory
