Abstract
A mathematical braid is a collection of crossings between n strings which flow continuously from right to left with fixed starting and end points. These crossing must be done in a specific manner in order to maintain structure. Specifically, after crossing that continue horizontally to the left. These will form a group, B_n, under concatenation. As a braid need not have a particular length, or number of crossings, this group is infinite in size and quite difficult to analyze. By turning our attention to the work done by William Thurston in [4], we see that the subset of positive braids, (B_n)^+, the problem is reduced. Specifically, using the Garside braid to generate a unique "factorization" of braids in order to create a structuring of B_n.
How to Cite
Haley, N., (2025) “The Garside Normal Form of The Braid Groups”, Capstone, The UNC Asheville Journal of Undergraduate Scholarship 38(1).
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