Representation and character varieties of the Baumslag-Solitar groups

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• 作者：V. V. Benyash-Krivets ; I. O. Govorushko
• 刊名：Proceedings of the Steklov Institute of Mathematics
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：292
• 期：1
• 页码：20-36
• 全文大小：1,524 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1531-8605
• 卷排序：292

文摘

Representation and character varieties of the Baumslag–Solitar groups BS(p, q) are analyzed. Irreducible components of these varieties are found, and their dimension is calculated. It is proved that all irreducible components of the representation variety R_n(BS(p, q)) are rational varieties of dimension n2, and each irreducible component of the character variety X_n(BS(p, q)) is a rational variety of dimension k ≤ n. The smoothness of irreducible components of the variety R_ns (BS(p, q)) of irreducible representations is established, and it is proved that all irreducible components of the variety R_ns (BS(p, q)) are isomorphic to A1 {0}.Original Russian Text © V.V. Benyash-Krivets, I.O. Govorushko, 2016, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Vol. 292, pp. 26–42.Dedicated to Academician V.P. Platonov on his 75th birthday