On the number of irreducible components of the representation variety of a family of one-relator groups

Martín-Morales, J. ; Oller-Marcén, A. M. (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1142/S0218196710005558

Año: 2010

Publicado en: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION 20, 1 (2010), 77-87
ISSN: 0218-1967

Factor impacto JCR: 0.537 (2010)

Categ. JCR: MATHEMATICS rank: 162 / 278 = 0.583 (2010) - Q3 - T2

Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2007-67884-C04- 02
Financiación: info:eu-repo/grantAgreement/ES/MICINN MTM2007-67908- C02-01

Tipo y forma: Article (PostPrint)

Área (Departamento): Área Didáctica Matemática (Dpto. Matemáticas)