Commentarii Mathematici Helvetici


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Volume 75, Issue 3, 2000, pp. 353–367
DOI: 10.1007/s000140050131

Additivity of tunnel number for small knots

J. Schultens

We show that for small knots $ K_1, K_2, t(K_1) + t(K_2) - 1 \leq t(K_1\#K_2) \leq t(K_1)+t(K_2)+1 $, and that for small knots $ K_1, \dots, K_n, t(K_1 \# \dots \# K_n) \geq n $.

Keywords: Small knot, tunnel number, decomposing annulus

Schultens J.: Additivity of tunnel number for small knots. Comment. Math. Helv. 75 (2000), 353-367. doi: 10.1007/s000140050131