Link invariants from finite racks

Sam Nelson

Displaying similar documents to “Link invariants from finite racks”

Vassiliev Invariants of Doodles, Ornaments, Etc.

Alexander B. Merkov (1999)

Publications de l'Institut Mathématique

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Finite type invariants of integral homology 3-spheres: A survey

Xiao-Song Lin (1998)

Banach Center Publications

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Invariants of $B$ -type links via an extension of the Kauffman bracket.

Kulish, P.P., Nikitin, A.M. (2000)

Zapiski Nauchnykh Seminarov POMI

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Link invariants from finite biracks

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...

Some New Invariants of Links.

Sadayoshi Kojima, Masyuki Yamasaki (1979)

Inventiones mathematicae

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Finite type invariants for cyclic equivalence classes of nanophrases

Yuka Kotorii (2014)

Fundamenta Mathematicae

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We define finite type invariants for cyclic equivalence classes of nanophrases and construct universal invariants. Also, we identify the universal finite type invariant of degree 1 essentially with the linking matrix. It is known that extended Arnold basic invariants to signed words are finite type invariants of degree 2, by Fujiwara's work. We give another proof of this result and show that those invariants do not provide the universal one of degree 2.

The Kontsevich integral and re-normalized link invariants arising from Lie superalgebras

Nathan Geer (2014)

Banach Center Publications

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We show that the coefficients of the re-normalized link invariants of [3] are Vassiliev invariants which give rise to a canonical family of weight systems.

Skein relations for Milnor's $μ$ -invariants.

Polyak, Michael (2005)

Algebraic & Geometric Topology

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On numerical invariants for knots in the solid torus

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...