Examples of tunnel number one knots which have the property ‘1 + 1 = 3’

Mathematical Proceedings of the Cambridge Philosophical Society - Tập 119 Số 1 - Trang 113-118 - 1996
Kanji Morimoto1, Masashi Sakuma2, Yoshiyuki Yokota3
1Department of Mathematics, Takushoku University, Tatemachi, Hachioji, Tokyo 193, Japan
2Department of Mathematics, Faculty of Science. Osaka University, Machikaneyama-cho 1-16, Toyonaka, Osaka 560, Japan
3Graduate School of Mathematics, Kyushu University, Fukuoka 812, Japan

Tóm tắt

Let K be a knot in the 3-sphere S3, N(K) the regular neighbourhood of K and E(K) = cl(S3−N(K)) the exterior of K. The tunnel number t(K) is the minimum number of mutually disjoint arcs properly embedded in E(K) such that the complementary space of a regular neighbourhood of the arcs is a handlebody. We call the family of arcs satisfying this condition an unknotting tunnel system for K. In particular, we call it an unknotting tunnel if the system consists of a single arc.

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Tài liệu tham khảo

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Mathematical Proceedings of the Cambridge Philosophical Society

Tập 119 Số 1

113-118

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