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The Word Problem for the Singular Braid Monoid

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arxiv math/9809070 v1 pith:RT4LPQ7X submitted 1998-09-12 math.GT math.GR

Oliver T. Dasbach , Bernd Gemein This is my paper · ORCID
classification math.GTmath.GR
keywords wordmonoidsingularbraidgroupproblemalgebraicallyalgorithm
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We give a solution to the word problem for the singular braid monoid SB_n. The complexity of the algorithm is quadratic in the product of the word length and the number of the singular generators in the word. Furthermore we algebraically reprove a result of Fenn, Keyman and Rourke that the monoid embeds into a group and we compute the cohomological dimension of this group.

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  1. Classification of Homogeneous Local Representations of the Singular Braid Monoid

    math.RT 2025-01 reject novelty 6.0 of 10

    The authors enumerate all non-trivial homogeneous 3-local representations of B_n for n≥4 and their 2- and 3-local extensions to the singular braid monoid SM_n.

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