Singular braids are isotopy classes of smooth strings which are allowed to cross each other pairwise with distinct tangents. Under the usual multiplication of braids, they form a monoid. The singular braid group was introduced by Fenn-Keyman-Rourke as the quotient group of the singular braid monoid. We give a solution of the word problem for this group. It is obtained as a combination of the results by Fenn-Keyman-Rourke and some simple geometric considerations based on the mapping class interpretation of braids. Combined with Corran's normal form for the singular braid monoid, our algorithm provides a computable normal form for the singular braid group.
Singular braid, word problem
OREVKOV, STEPAN YU. (2004) "Solution of the Word Problem in the Singular Braid Group," Turkish Journal of Mathematics: Vol. 28: No. 1, Article 7. Available at: https://journals.tubitak.gov.tr/math/vol28/iss1/7