Link concordance invariants and homotopy theory.
T.D. Cochran (1987)
Inventiones mathematicae
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T.D. Cochran (1987)
Inventiones mathematicae
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Alexander B. Merkov (1999)
Publications de l'Institut Mathématique
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Slavik Jablan (2000)
Visual Mathematics
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Kulish, P.P., Nikitin, A.M. (2000)
Zapiski Nauchnykh Seminarov POMI
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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.
Xiao-Song Lin (1998)
Banach Center Publications
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Mangum, Brian, Stanford, Theodore (2001)
Algebraic & Geometric Topology
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Sam Nelson (2014)
Banach Center Publications
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A birack is an algebraic structure with axioms encoding the blackboard-framed Reidemeister moves, incorporating quandles, racks, strong biquandles and semiquandles as special cases. In this paper we extend the counting invariant for finite racks to the case of finite biracks. We introduce a family of biracks generalizing Alexander quandles, (t,s)-racks, Alexander biquandles and Silver-Williams switches, known as (τ,σ,ρ)-biracks. We consider enhancements of the counting invariant using...
Kent E. Orr (1989)
Inventiones mathematicae
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Sadayoshi Kojima, Masyuki Yamasaki (1979)
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...
Habiro, Kazuo (2000)
Geometry & Topology
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