132071 20240301161205.0 doi 10.1142/S0218196710005558 sideral 71743 ART-2010-71743 eng Martín-Morales, J. (orcid)0000-0002-6559-4722 On the number of irreducible components of the representation variety of a family of one-relator groups 2010 Let us consider the group G = 〈x, y | xm = yn〉 with m and n nonzero integers. The set R(G) of representations of G over SL(2, ℂ) is a four-dimensional algebraic variety which is an invariant of G. In this paper the number of irreducible components of R(G) together with their dimensions are computed. We also study the set of metabelian representations of this family of groups. Finally, the behavior of the projection t : R(G) → X(G), where X(G) is the character variety of the group, and some combinatorial aspects of R(G) are investigated. Access copy available to the general public Unrestricted info:eu-repo/grantAgreement/ES/MICINN/MTM2007-67884-C04- 02 info:eu-repo/grantAgreement/ES/MICINN MTM2007-67908- C02-01 info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 0.537 2010 MATHEMATICS 162 / 278 = 0.583 2010 Q3 T2 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Oller-Marcén, A. M. Universidad de Zaragoza (orcid)0000-0002-8191-3199 2006 200 Universidad de Zaragoza Dpto. Matemáticas Área Didáctica Matemática 20, 1 (2010), 77-87 Int. J. Algebr. Comput. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION 0218-1967 391604 http://zaguan.unizar.es/record/132071/files/texto_completo.pdf Postprint 1374923 http://zaguan.unizar.es/record/132071/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:132071 articulos driver 2024-03-01-14:37:05 ARTICLE