State Models and the Jones Polynomial

Kauffman, L. H. (1987). State Models and the Jones Polynomial. Topology, 395-407.

Type

Journal article

Intellectual base

Primary research

Year

1987

Pages

395-407

ISSN

0040-9383

DOI

10.1016/0040-9383(87)90009-7

DOI registrant

Elsevier

Link

https://doi.org/10.1016/0040-9383(87)90009-7

Cited by

2 citations across 2 artifacts.

Each citation links to the sentence it supports in the citing article.

Domain-specific

• Knot Polynomial
  • Not the unnormalized Kauffman bracket as an ambient-isotopy invariant. The bracket is invariant under Reidemeister II and III—regular isotopy—but changes under Reidemeister I. A writhe-dependent normalization produces the Jones polynomial, which is an ambient-isotopy invariant.
• Temperley–Lieb Algebra
  • Under a parameter-dependent linear combination of identity and \(e_i\), however, braid generators can be represented in a Temperley–Lieb algebra

    This sourceKauffman's bracket resolves each crossing into A times one planar smoothing plus A^{-1} times the other - the identity and cup-cap diagrams - which is the linear combination that lands the braid generators in the Temperley-Lieb algebra.

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