Mapping class group of a surface is generated by two elements
نویسندگان
چکیده
منابع مشابه
The Mapping Class Group of a Punctured Surface Is Generated by Three Elements
Let Σg,p be a closed oriented surface of genus g ≥ 1 with p punctures. Let Mod(Σg,p) be the mapping class group of Σg,p. Wajnryb proved in [Wa] that for p = 0, 1 Mod(Σg,p) is generated by two elements. Korkmaz proved in [Ko] that one of these generators can be taken as a Dehn twist. For p ≥ 2, We proved that Mod(Σg,p) is generated by three elements.
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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.
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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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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...
متن کامل0 Torsion Elements in the Mapping Class Group of a Surface
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ژورنال
عنوان ژورنال: Topology
سال: 1996
ISSN: 0040-9383
DOI: 10.1016/0040-9383(95)00037-2