TY - JOUR

T1 - Four-genus and four-dimensional clasp number of a knot

AU - Murakami, Hitoshi

AU - Yasuhara, Akira

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

KW - 4-dimensional clasp number

KW - 4-genus

KW - Linking form

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U2 - 10.1090/s0002-9939-00-05461-7

DO - 10.1090/s0002-9939-00-05461-7

M3 - Article

AN - SCOPUS:23044521880

SN - 0002-9939

VL - 128

SP - 3693

EP - 3699

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 12

ER -