Braid Word

Any -braid is expressed as a braid word, e.g., is a braid wordfor the Braid Group . By Alexander's Theorem, any Link is representable by a closed braid, butthere is no general procedure for reducing a braid word to its simplest form. However, Markov's Theorem gives aprocedure for identifying different braid words which represent the same Link.

Let be the sum of Positive exponents, and the sum of Negative exponents in the Braid Group .If

References

Jones, V. F. R. ``A Polynomial Invariant for Knots via von Neumann Algebras.'' Bull. Amer. Math. Soc. 12, 103-111, 1985.

Jones, V. F. R. ``Hecke Algebra Representations of Braid Groups and Link Polynomials.'' Ann. Math. 126, 335-388, 1987.

• Annihilator
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