Rym Karoui's research while affiliated with Université de Montpellier and other places

Publications (2)

Braid groups and mapping class groups have many features in common. Similarly to the notion of inverse braid monoid inverse mapping class monoid is defined. It concerns surfaces with punctures, but among given $n$ punctures several can be omitted. This corresponds to braids where the number of strings is not fixed. In the paper we give the analogue...
Pure braid groups and pure mapping class groups of a punctured sphere have many features in common. In the paper the graded Lie algebra of the descending central series of the pure mapping class of a sphere is studied. A simple presentation of this Lie algebra is obtained.


... We will introduce the notion of PM -mapping class monoids and observe the relation to the braid PM -monoid. The construction of PM -mapping class monoid is an analogy of inverse mapping class monoid defined by R. Karoui and V. V. Vershinin [26]. There exists an important theorem in the theory of mapping class group called Dehn-Nilsen-Baer theorem. ...