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

Hitoshi Murakami, Akira Yasuhara

研究成果: Article

19 引用 (Scopus)


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.

ジャーナルProceedings of the American Mathematical Society
出版物ステータスPublished - 2000 12 1

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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