Tunnel number degeneration under the connected sum of prime knots
arXiv:1303.7275 · doi:10.1016/j.topol.2013.03.010
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.
arXiv comment40 pages, 28 figures; Version 2: reference added, minor changes in text
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