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

Hitoshi Murakami, Akira Yasuhara

Research output: Contribution to journalArticlepeer-review

30 Citations (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.

Original languageEnglish
Pages (from-to)3693-3699
Number of pages7
JournalProceedings of the American Mathematical Society
Issue number12
Publication statusPublished - 2000


  • 4-dimensional clasp number
  • 4-genus
  • Linking form


Dive into the research topics of 'Four-genus and four-dimensional clasp number of a knot'. Together they form a unique fingerprint.

Cite this