抄録
For a knot K in the 3-sphere, by using the linking form on the first homology group of the double branched cover of the 3-sphere, we investigate some numerical invariants, 4-genus g* (K), nonorientable 4-genus γ*(K) and 4-dimensional clasp number c* (K), defined from the four-dimensional viewpoint. T. Shibuya gave an inequality g*(K) ≤ c*(K), and asked whether the equality holds or not. From our result in this paper, we find that the equality does not hold in general.
| 元の言語 | English |
|---|---|
| ページ（範囲） | 3693-3699 |
| ページ数 | 7 |
| ジャーナル | Proceedings of the American Mathematical Society |
| 巻 | 128 |
| 発行部数 | 12 |
| 出版物ステータス | Published - 2000 12 1 |
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ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
これを引用
Four-genus and four-dimensional clasp number of a knot. / Murakami, Hitoshi; Yasuhara, Akira.
：: Proceedings of the American Mathematical Society, 巻 128, 番号 12, 01.12.2000, p. 3693-3699.研究成果: Article
}
TY - JOUR
T1 - Four-genus and four-dimensional clasp number of a knot
AU - Murakami, Hitoshi
AU - Yasuhara, Akira
PY - 2000/12/1
Y1 - 2000/12/1
N2 - For a knot K in the 3-sphere, by using the linking form on the first homology group of the double branched cover of the 3-sphere, we investigate some numerical invariants, 4-genus g* (K), nonorientable 4-genus γ*(K) and 4-dimensional clasp number c* (K), defined from the four-dimensional viewpoint. T. Shibuya gave an inequality g*(K) ≤ c*(K), and asked whether the equality holds or not. From our result in this paper, we find that the equality does not hold in general.
AB - For a knot K in the 3-sphere, by using the linking form on the first homology group of the double branched cover of the 3-sphere, we investigate some numerical invariants, 4-genus g* (K), nonorientable 4-genus γ*(K) and 4-dimensional clasp number c* (K), defined from the four-dimensional viewpoint. T. Shibuya gave an inequality g*(K) ≤ c*(K), and asked whether the equality holds or not. From our result in this paper, we find that the equality does not hold in general.
KW - 4-dimensional clasp number
KW - 4-genus
KW - Linking form
UR - http://www.scopus.com/inward/record.url?scp=23044521880&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=23044521880&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:23044521880
VL - 128
SP - 3693
EP - 3699
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 12
ER -