On the linearity of certain mapping class groups

Abstract

S. Bigelow proved that the braid groups are linear. That is, there is a faithful representation of the braid group into the general linear group of some field. Using this, we deduce from previously known results that the mapping class group of a sphere with punctures and hyperelliptic mapping class groups are linear. In particular, the mapping class group of a closed orientable surface of genus 2 is linear.

5 pages, 1 figure, to apper in Turkish Journal of Mathematics

Cited by in corpus (12)

• The mapping class group from the viewpoint of measure equivalence theory
• The mapping class group of a genus two surface is linear
• The Birman-Hilden theory
• Embeddings of the braid groups of covering spaces, classification of the finite subgroups of the braid groups of the real projective plane, and linearity of braid groups of low-genus surfaces
• On the linearity problem for mapping class groups
• A survey of surface braid groups and the lower algebraic K-theory of their group rings
• The symplectic representation of the mapping class group is unique
• An effective Lie--Kolchin theorem for quasi-unipotent matrices
• Remarks on the faithfulness of the Jones representations
• On visualization of the linearity problem for mapping class groups of surfaces
• On the image of the Lawrence-Krammer representation
• The hyperelliptic mapping class group of a nonorientable surface of genus $g\ge 4$ has a faithful representation into $GL(g^2-1,\mathbb{R})$