An elementary approach to the mapping class group of a surface.
This is a survey of some consequences of the fact that the fundamental group of the orbifold with singular set the Borromean link and isotropy cyclic of order 4 is a universal kleinian group.
Using the notion of relative presentation due to Bogley and Pride, we give a new proof of a theorem of Prishchepov on the asphericity of certain symmetric presentations of groups. Then we obtain further results and applications to topology of low-dimensional manifolds.