Tunnel numbers of small knots

do not go down under connected sum

Authors:
Kanji Morimoto and Jennifer Schultens

Journal:
Proc. Amer. Math. Soc. **128** (2000), 269-278

MSC (1991):
Primary 57M25, 57N10

Published electronically:
September 9, 1999

MathSciNet review:
1641065

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let and be two knots in and , the tunnel numbers of them. In this paper, we show that if both and are small, then . Moreover we show that for any small knots .

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Additional Information

**Kanji Morimoto**

Affiliation:
Department of Mathematics, Takushoku University Tatemachi, Hachioji, Tokyo 193, Japan

Email:
morimoto@la.takushoku-u.ac.jp

**Jennifer Schultens**

Affiliation:
Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322

Email:
jcs@mathcs.emory.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-99-05160-6

Keywords:
Knots,
connected sum,
tunnel number

Received by editor(s):
March 1, 1998

Published electronically:
September 9, 1999

Communicated by:
Ronald A. Fintushel

Article copyright:
© Copyright 1999
American Mathematical Society