Non-additivity for triple point numbers on the connected sum of surface-knots
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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, $\textrm {t}(F)$, 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.References
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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
- Email: satoh@math.s.chiba-u.ac.jp
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 613-616
- MSC (2000): Primary 57Q45; Secondary 57Q35
- DOI: https://doi.org/10.1090/S0002-9939-04-07522-7
- MathSciNet review: 2093086