Definition:Braid Theory
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Definition
Braid theory studies the number of different ways a number of cords can be braided.
Also see
- Results about braid theory can be found here.
Historical Note
Emil Artin related the study of braids to group theory in the $1930$s.
In the $1960$s, Vladimir Igorevich Arnold pointed out the relevance of braid theory the theory of mappings.
Thus, if $n$ points are moved continuously in the plane back to their original positions, the motion can be interpreted as a braid.
Hence Arnold showed how the roots of a polynomial vary according to how the polynomial coefficients are varied.
Also in the $1930$s, James Waddell Alexander II established the close relationship between braid theory and knot theory.
This was then exploited in the $1980$s by Vaughan Frederick Randal Jones.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): braid
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): braid