The mapping class group of a genus two surface is linear Stephen
نویسندگان
چکیده
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 close relationship between this group and Bn−1 . We then extend this to a faithful representation of the mapping class group of the genus two surface, using Birman and Hilden’s result that this group is a Z2 central extension of the mapping class group of the 6-punctured sphere. The resulting representation has dimension sixty-four and will be described explicitly. In closing we will remark on subgroups of mapping class groups which can be shown to be linear using similar techniques. AMS Classification 20F36; 57M07, 20C15
منابع مشابه
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...
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