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arXiv · 1303.7275

Tunnel number degeneration under the connected sum of prime knots

João Miguel Nogueira
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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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João Miguel Nogueira. 2013-06-17. Tunnel number degeneration under the connected sum of prime knots. https://doi.org/10.1016/j.topol.2013.03.010

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