The mapping class group of a genus two surface is linear

The Mapping Class Group of a Genus Two Surface Is Linear

In this paper we construct a faithful representation of the mapping class group of the genus two surface into a group of matrices over the complex numbers. Our starting point is the Lawrence-Krammer representation of the braid group Bn , which was shown to be faithful by Bigelow and Krammer. We obtain a faithful representation of the mapping class group of the n-punctured sphere by using the cl...

The mapping class group of a genus two surface is linear Stephen

In this paper we construct a faithful representation of the mapping class group of the genus two surface into a group of matrices over the complex numbers. Our starting point is the Lawrence-Krammer representation of the braid group Bn , which was shown to be faithful by Bigelow and Krammer. We obtain a faithful representation of the mapping class group of the n-punctured sphere by using the cl...

The Mapping Class Group of a Genus

Generating the Surface Mapping Class Group by Two Elements

Wajnryb proved in [W2] that the mapping class group of an orientable surface is generated by two elements. We prove that one of these generators can be taken as a Dehn twist. We also prove that the extended mapping class group is generated by two elements, again one of which is a Dehn twist.

A Faithful Linear-categorical Action of the Mapping Class Group of a Surface with Boundary

We show that the action of the mapping class group on bordered Floer homology in the second to extremal spin-structure is faithful. The paper is self-contained, and in particular does not assume any background in Floer homology.