Displaying similar documents to “Link invariants from finite biracks”

Link invariants from finite racks

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.

Vassiliev invariants as polynomials

Simon Willerton (1998)

Banach Center Publications

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Three results are shown which demonstrate how Vassiliev invariants behave like polynomials.

Homfly polynomials as vassiliev link invariants

Taizo Kanenobu, Yasuyuki Miyazawa (1998)

Banach Center Publications

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We prove that the number of linearly independent Vassiliev invariants for an r-component link of order n, which derived from the HOMFLY polynomial, is greater than or equal to min{n,[(n+r-1)/2]}.

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...

A conjecture on Khovanov's invariants

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.