Any -braid is expressed as a braid word, e.g., is a braid word for the Braid Group . By Alexander's Theorem, any Link is representable by a closed braid, but there is no general procedure for reducing a braid word to its simplest form. However, Markov's Theorem gives a procedure 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

then the closed braid is not Amphichiral (Jones 1985).

**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.

© 1996-9

1999-05-26