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

DOI:
https://doi.org/10.1090/S0002-9939-04-07522-7

Published electronically:
August 30, 2004

MathSciNet review:
2093086

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Any surface-knot in 4-space can be projected into 3-space with a finite number of triple points, and its triple point number, , is defined similarly to the crossing number of a classical knot. By definition, we have 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

Email:
satoh@math.s.chiba-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-04-07522-7

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