Combinatorial Aspects of the Character Variety of a Family of One-Relator Groups

Martin-Morales, J. (Universidad de Zaragoza) ; Oller-Marcen,A. M. (Universidad de Zaragoza)

Resumen: Let us consider the group G = hx, y | x m = y ni with m and n nonzero integers. In this paper, we study the character variety X(G) in SL(2, C) of the group G, obtaining by elementary methods an explicit primary decomposition of the ideal corresponding to X(G) in the coordinates X = tx, Y = ty and Z = txy. As an easy consequence, a formula for computing the number of irreducible components of X(G) as a function of m and n is given. Finally we
provide a combinatorial description of X(G) and we prove that in most cases it is possible to recover (m, n) from the combinatorial structure of X(G).

Idioma: Inglés

DOI: 10.1016/j.topol.2009.06.011

Año: 2009

Publicado en: TOPOLOGY AND ITS APPLICATIONS 156, 14 (2009), 2376-2389
ISSN: 0166-8641

Factor impacto JCR: 0.441 (2009)

Categ. JCR: MATHEMATICS rank: 191 / 255 = 0.749 (2009) - Q3 - T3
Categ. JCR: MATHEMATICS, APPLIED rank: 177 / 204 = 0.868 (2009) - Q4 - T3

Financiación: info:eu-repo/grantAgreement/ES/DGA/E15
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 Geometría y Topología (Dpto. Matemáticas)
Área (Departamento): Área Didáctica Matemática (Dpto. Matemáticas)