Separating twists and the Magnus representation

Aaron Pixton (Cambridge University / Princeton University)

Wednesday 18th March, 2009 16:00-17:00 Mathematics Building, room 214


The mapping class group of a surface is the group of isotopy classes of self-homeomorphisms of the surface. One way of studying this group is through the Magnus representation, which is a linear representation of a subgroup of the mapping class group. I will describe a few equivalent definitions of this representation, and then I will classify all relations between the images of two separating Dehn twists under the Magnus representation. In particular, it turns out that the image of the Magnus representation contains many free groups of rank two. (Joint work with Thomas Church.)

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