Four-genus and four-dimensional clasp number of a knot

Hitoshi Murakami, Akira Yasuhara

研究成果: Article

19 引用 (Scopus)

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
128
発行部数12
出版物ステータスPublished - 2000 12 1

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Knot
Genus
Equality
Branched Cover
Homology Groups
Linking
Invariant
Form

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

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