Event № 1320

We are interested in some quotients of the mapping class group G of a compact surface of genus at least 2. More precisely, given a subset S of G and an integer n we study the quotient obtained by "killing" the n-th power of every element of S. In particular, we will consider the case where S is the set of all Dehn twists or all pseudo-Anosov elements. As an example we provide infinite quotients of mapping class groups where a fixed power of every pseudo-Anosov homeomorphism is identified with a periodic or reducible element. The techniques that we will present can also be used to exhibit partial periodic quotients of many groups acting on a hyperbolic space.