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Braid groups are linear | | Daan Krammer
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11 May 2004 | | Journal: | Ann. of Math. (2), Vol. 155 (2002), no. 1, 131--156 | | Subject: | Group Theory; Geometric Topology | math.GR math.GT | | Abstract: | In a previous work [11], the author considered a representation of the braid group
ho: B_n o GL_m(Bbb Z[q^{pm 1},t^{pm 1}]) (m=n(n-1)/2), and proved it to be faithful for n=4. Bigelow [3] then proved the same representation to be faithful for all n by a beautiful topological argument. The present paper gives a different proof of the faithfulness for all n. We establish a relation between the Charney length in the braid group and exponents of t. A certain B_n-invariant subset of the module is constructed whose properties resemble those of convex cones. We relate line segments in this set with the Thurston normal form of a braid. | | Source: | arXiv, math.GR/0405198 | | Services: | Forum | Review | PDF | Favorites | |
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