Solving the Word Problem in the Merge-and-Part Braid Monoid
by
James East
University of Sydney

In 1925 Emil Artin published a paper entitled Theorie der Zöpfe (Theory of Braids). In it, he introduced the braid group B_n, gave a group presentation of B_n, and solved the word problem. This enables one to determine whether two given geometric braids are homotopy equivalent. In recent times, ``braid analogues'' of various important semigroups related to the symmetric group (eg. the full transformation semigroup T_n, and the symmetric inverse semigroup I_n) have been defined, presentations given, and word problems solved. In this talk we introduce the merge-and-part braid monoid F B_n. This monoid is a braid analogue of F_n, the monoid of uniform block bijections on an n-set. We will state a presentation of FB_n and indicate an elegant solution to the word problem.

Date received: September 16, 2003