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.
|Number of pages||7|
|Journal||Proceedings of the American Mathematical Society|
|Publication status||Published - 2000 Dec 1|
- 4-dimensional clasp number
- Linking form
ASJC Scopus subject areas
- Applied Mathematics