ADDITIVITY OF TUNNEL NUMBER FOR SMALL KNOTS

JENNIFER SCHULTENS

Abstract. We show that for small knots K_{1}, K_{2}, t(K_{1})+t(K_{2})−1 ≤ t(K_{1}#K_{2}) ≤ t(K_{1}) + t(K_{2}) + 1, and that for small knots K_{1}, …, K_{n}, t(K_{1}# … #K_{n}) ≥ n.