doi:10.1142/S0218196710005558engMartín-Morales, J.Oller-Marcén, A. M.On the number of irreducible components of the representation variety of a family of one-relator groupsART-2010-71743Let 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.2010http://zaguan.unizar.es/record/13207110.1142/S0218196710005558http://zaguan.unizar.es/record/132071oai:zaguan.unizar.es:132071info:eu-repo/grantAgreement/ES/MICINN/MTM2007-67884-C04- 02info:eu-repo/grantAgreement/ES/MICINN MTM2007-67908- C02-01INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION 20, 1 (2010), 77-87All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess