by S.Yu. Orevkov
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.