. A G ] 1 8 A pr 2 00 9 Mapping class groups are linear Igor
نویسنده
چکیده
It is shown, that the mapping class group of a surface of the genus g ≥ 2 admits a faithful representation into the matrix group GL6g−6(Z). The proof is based on a categorical correspondence between the Riemann surfaces and the AF -algebras.
منابع مشابه
2 8 Ju l 2 00 6 K - theory of the mapping class groups
We use the K-theory of operator algebras to settle the Harvey conjecture for a special family of the mapping class groups. Namely, we first establish a relationship between the Riemann surfaces and the dimension groups, and then prove that the mapping class group of a surface of genus g with n holes, is a linear arithmetic group of rank 6g − 6 + 2n.
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We use the K-theory of operator algebras to partially settle the Harvey conjecture for the mapping class groups. Namely, we first establish a relationship between the Riemann surfaces and the dimension groups, and then prove that modulo the Torelli group, the mapping class group of a surface of genus g with n holes, is a linear arithmetic group of the rank 6g − 6 + 2n.
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