On the linearity of certain mapping class groups. (English) Zbl 0965.57013

Summary: S. J. Bigelow [Braid groups are linear, J. Am. Math. Soc. 14, No. 2, 471-486 (2001)] 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.


57M99 General low-dimensional topology
20F38 Other groups related to topology or analysis
57M60 Group actions on manifolds and cell complexes in low dimensions
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
20F34 Fundamental groups and their automorphisms (group-theoretic aspects)
20F36 Braid groups; Artin groups
30F99 Riemann surfaces
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