On the Lie Algebras Associated with Pure Mapping Class Groups
نویسنده
چکیده
Mapping class group is an important object in Topology, Complex Analysis, Algebraic Geometry and other domains. It is a lucky case when the method of Algebraic Topology works perfectly well, the application of the functor of fundamental group completely solves the topological problem: group of isotopy classes of homeomorphisms is described in terms of automorphisms of the fundamental group of the corresponding surface, as states the Dehn-Nilsen-Baer theorem, see [15], for example. Let Sg,b,n be an oriented surface of the genus g with b boundary components and with a set Qn of n fixed points. Consider the group Homeo(Sg,b,n) of orientation preserving selfhomeomorphisms of Sg,b,n which fix pointwise the boundary (if it exists) and map the set Qn into itself. Orientation reversing homeomorphisms also possible to consider, see [8], for example, but we restrict ourselves to orientation preserving case. Let Homeo0(Sg,b,n) be the normal subgroup of self-homeomorphisms of Sg,b,n which are isotopic to identity. Then the mapping class group Mg,b,n is defined as a factor group
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