There are knots whose tunnel numbers go down under connected sum

Morimoto, Kanji

doi:10.1090/S0002-9939-1995-1317043-4

There are knots whose tunnel numbers go down under connected sum
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Proc. Amer. Math. Soc. 123 (1995), 3527-3532 Request permission

Abstract:

In this paper, we show that there are infinitely many tunnel number two knots K such that the tunnel number of $K\# K’$ is equal to two again for any 2-bridge knot $K’$.

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