Non-additivity for triple point numbers on the connected sum of surface-knots

Satoh, Shin

doi:10.1090/S0002-9939-04-07522-7

Non-additivity for triple point numbers on the connected sum of surface-knots
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Proc. Amer. Math. Soc. 133 (2005), 613-616 Request permission

Abstract:

Any surface-knot $F$ in 4-space can be projected into 3-space with a finite number of triple points, and its triple point number, $\textrm {t}(F)$, is defined similarly to the crossing number of a classical knot. By definition, we have $\textrm {t}(F_1\# F_2)\leq \textrm {t}(F_1)+\textrm {t}(F_2)$ 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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