Tunnel number degeneration under the connected sum of prime knots
classification
🧮 math.GT
keywords
knotsnumbertunnelconnectedprimeapplicationconjectureconstruct
read the original abstract
We study 2-string free tangle decompositions of knots with tunnel number two. As an application, we construct infinitely many counter-examples to a conjecture in the literature stating that the tunnel number of the connected sum of prime knots doesn't degenerate by more than one.
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