Pure Maths Colloquium: Mapping Class Groups of Surfaces
8 November 2010 17:15 in CM221
The mapping class group is the automorphism group of a surface, and is a fundamental object in low-dimensional topology, geometric group theory, algebraic geometry, and complex analysis. In particular, it arises naturally as a subgroup of the automorphism group of a free group, as the (orbifold) fundamental group of the moduli space of Riemann surfaces, and as a means of encoding the structure of all 3-manifolds (via Heegaard splittings) and a large class of 4-manifolds (via Lefschetz pencils). In this talk we will give an introduction to the structure of these groups, including a certain subgroup known as the Torelli group.
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