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

Hitoshi Murakami, Akira Yasuhara

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

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
Volume128
Issue number12
Publication statusPublished - 2000 Dec 1

Fingerprint

Knot
Genus
Equality
Branched Cover
Homology Groups
Linking
Invariant
Form

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Four-genus and four-dimensional clasp number of a knot. / Murakami, Hitoshi; Yasuhara, Akira.

In: Proceedings of the American Mathematical Society, Vol. 128, No. 12, 01.12.2000, p. 3693-3699.

Research output: Contribution to journalArticle

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