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
VL - 128
SP - 3693
EP - 3699
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 12
ER -