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

Author: Shin Satoh
Journal: Proc. Amer. Math. Soc. 133 (2005), 613-616
MSC (2000): Primary 57Q45; Secondary 57Q35
Published electronically: August 30, 2004
MathSciNet review: 2093086
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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, ${\rm t}(F)$, is defined similarly to the crossing number of a classical knot. By definition, we have ${\rm t}(F_1\char93 F_2)\leq {\rm t}(F_1)+{\rm t}(F_2)$ 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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Additional Information

Shin Satoh
Affiliation: Graduate School of Science and Technology, Chiba University, Yayoi-cho 1-33, Inage-ku, Chiba, 263-8522, Japan

Keywords: Surface-knot, connected sum, triple point, twist-spun knot.
Received by editor(s): July 27, 2003
Received by editor(s) in revised form: August 29, 2003
Published electronically: August 30, 2004
Communicated by: Ronald A.Fintushel
Article copyright: © Copyright 2004 American Mathematical Society

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