Displaying similar documents to “Finite type invariants of integral homology 3-spheres: A survey”

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.

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...

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 gauge-field approach to 3- and 4-manifold invariants

Bogusław Broda (1997)

Banach Center Publications

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An approach to construction of topological invariants of the Reshetikhin-Turaev-Witten type of 3- and 4-dimensional manifolds in the framework of SU(2) Chern-Simons gauge theory and its hidden (quantum) gauge symmetry is presented.

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]}.