Abstract
The word problem of a group is an important question. The word problem in the braid group is of particular interest for topologists, algebraists and geometers. In [7] we have looked at the braid group from a topological point of view, and thus using a new computerized representation of some elements of the fundamental group we gave a solution for its word problem. In this paper we will give an algorithm that will make it possible to transform the new geometric presentation from [7] into a syntactic one. This will make it possible to computerize the group operation to sets of elements of the fundamental group, called a g-base, which are isomorphic to the braid group. Moreover, we will show that it is sufficient enough to look at the syntactic presentation in order to solve the braid word problem, resulting with a faster braid word solution.
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© 2003 Hindustan Book Agency
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Kaplan, S., Teicher, M. (2003). Solving the Braid Word Problem Via the Fundamental Group. In: Musili, C. (eds) Advances in Algebra and Geometry. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-12-5_19
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DOI: https://doi.org/10.1007/978-93-86279-12-5_19
Publisher Name: Hindustan Book Agency, Gurgaon
Print ISBN: 978-81-85931-36-4
Online ISBN: 978-93-86279-12-5
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