After this paper was published, the following information about doodles was pointed out by Roger Fenn. A doodle was introduced by Fenn and Taylor , which is a finite collection of closed curves without triple intersections on a closed oriented surface considered up to the second flat Reidemeister moves with the condition (*) that each component has no self-intersections. Khovanov  introduced doodle groups, and for his process, he considered doodles under a more generalized setting (i.e. removing the condition (*) and permitting the first flat Reidemeister moves). He showed [4, Theorem 2.2], a result similar to our [3, Theorem 2.2(c)]. He also pointed out that [1, Corollary 2.8.9] gives a result similar to [4, Theorem 2.2].
The authors first noticed the above results by Fenn and Khovanov via personal communication with Fenn, and therefore, the authors would like to thank Roger Fenn for these references.
ASJC Scopus subject areas
- Algebra and Number Theory