The length of unknotting tunnels
Daryl Cooper, Marc Lackenby, Jessica S. Purcell
TL;DR
This paper demonstrates that there are hyperbolic 3-manifolds with tunnel number one that possess arbitrarily long unknotting tunnels, challenging previous assumptions in the field.
Contribution
It constructs examples of hyperbolic 3-manifolds with arbitrarily long unknotting tunnels, answering a longstanding question negatively.
Findings
Existence of hyperbolic 3-manifolds with arbitrarily long unknotting tunnels
Counterexample to previous conjectures about unknotting tunnel lengths
Advancement in understanding the geometry of 3-manifolds
Abstract
We show there exist tunnel number one hyperbolic 3-manifolds with arbitrarily long unknotting tunnel. This provides a negative answer to an old question of Colin Adams.
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