Invariants of Knot Cobordism.
J. LEVINE (1969)
Inventiones mathematicae
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J. LEVINE (1969)
Inventiones mathematicae
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T.D. Cochran (1987)
Inventiones mathematicae
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Joan S. Birman, W.W. Menasco (1990)
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T.D. Cochran (1985)
Inventiones mathematicae
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George R. Kempf (1993)
Inventiones mathematicae
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V.G. Turaev (1988)
Inventiones mathematicae
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Alexander B. Merkov (1999)
Publications de l'Institut Mathématique
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Sam Nelson (2014)
Fundamenta Mathematicae
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We define ambient isotopy invariants of oriented knots and links using the counting invariants of framed links defined by finite racks. These invariants reduce to the usual quandle counting invariant when the rack in question is a quandle. We are able to further enhance these counting invariants with 2-cocycles from the coloring rack's second rack cohomology satisfying a new degeneracy condition which reduces to the usual case for quandles.
Kent E. Orr (1989)
Inventiones mathematicae
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Khaled Bataineh (2015)
Open Mathematics
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We define some new numerical invariants for knots with zero winding number in the solid torus. These invariants explore some geometric features of knots embedded in the solid torus. We characterize these invariants and interpret them on the level of the knot projection. We also find some relations among some of these invariants. Moreover, we give lower bounds for some of these invariants using Vassiliev invariants of type one. We connect our invariants to the bridge number in the solid...
Stavros Garoufalidis (2004)
Fundamenta Mathematicae
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We formulate a conjectural formula for Khovanov's invariants of alternating knots in terms of the Jones polynomial and the signature of the knot.
Uwe Kaiser (1992)
Manuscripta mathematica
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