Surface knot theory and related groups

Study of certain isotopy classes of a finite collection of immersed circles without triple or higher intersections on closed oriented surfaces can be thought of as a planar analogue of virtual knot theory where the genus zero case corresponds to classical knot theory. It is intriguing to know which class of groups serves the purpose that Artin braid groups serve in classical knot theory. Mikhail Khovanov proved that twin groups, a class of right angled Coxeter groups with only far commutativity relations, do the job for genus zero case. A recent work shows that an appropriate class of groups called virtual twin groups fits into the theory for higher genus cases. The talk would give an overview of some recent developments along these lines.