- Turkish Journal of Mathematics
- Vol: 28 Issue: 1
- Solution of the Word Problem in the Singular Braid Group
Solution of the Word Problem in the Singular Braid Group
Authors : Stepan Yu. Orevkov
Pages : 95-100
View : 7 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :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.Keywords : Singular braid, word problem