On the first cohomology of automorphism groups of graph groups

Aramayona, Javier ; Martínez Pérez, Concepción María (Universidad de Zaragoza)

Resumen: We study the (virtual) indicability of the automorphism group Aut(AΓ) of the right-angled Artin group AΓ associated to a simplicial graph Γ. First, we identify two conditions -- denoted (B1) and (B2) -- on Γ which together imply that H1(G,Z)=0 for certain finite-index subgroups G<Aut(AΓ). On the other hand we will show that (B2) is equivalent to the matrix group H=Im(Aut(AΓ)→Aut(H1(AΓ)))<GL(n,Z) not being virtually indicable, and also to H having Kazhdan's property (T). As a consequence, Aut(AΓ) virtually surjects onto Z whenever Γ does not satisfy (B2). In addition, we give an extra property of Γ ensuring that Aut(AΓ) and Out(AΓ) virtually surject onto Z. Finally, in the appendix we offer some remarks on the linearity problem for Aut(AΓ).

Idioma: Inglés

DOI: 10.1016/j.jalgebra.2015.11.045

Año: 2016

Publicado en: JOURNAL OF ALGEBRA 452 (2016), 17-41
ISSN: 0021-8693

Factor impacto JCR: 0.61 (2016)

Categ. JCR: MATHEMATICS rank: 168 / 310 = 0.542 (2016) - Q3 - T2

Factor impacto SCIMAGO: 1.266 - Algebra and Number Theory (Q1)

Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2010-19938-C03-03

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Algebra (Dpto. Matemáticas)