Abstract
Any surface-knot F F in 4-space can be projected into 3-space with a finite number of triple points, and its triple point number, t ( F ) \textrm {t}(F) , is defined similarly to the crossing number of a classical knot. By definition, we have t ( F 1 # F 2 ) ≤ t ( F 1 ) + t ( F 2 ) \textrm {t}(F_1\# F_2)\leq \textrm {t}(F_1)+\textrm {t}(F_2) for the connected sum. In this paper, we give infinitely many pairs of surface-knots for which this equality does not hold.
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