On right-angled Artin groups whose underlying graphs have two vertices with the same link
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Let Γ be a graph which contains two vertices a, b with the same link. For the case where the link has less than 3 vertices, we prove that if the right-angled Artin group A(Γ) contains a hyperbolic surface subgroup, then A(Γ−{a}) contains a hyperbolic surface subgroup. More- over, we also show that the same result holds with certain restrictions for the case where the link has more than or equal to 3 vertices.
Abstract
Let Γ be a graph which contains two vertices a, b with the same link. For the case where the link has less than 3 vertices, we prove that if the right-angled Artin group A(Γ) contains a hyperbolic surface subgroup, then A(Γ−{a}) contains a hyperbolic surface subgroup. More- over, we also show that the same result holds with certain restrictions for the case where the link has more than or equal to 3 vertices.
참고문헌 (12)
- "Combinatorial methods for detecting surface subgroups in right-angled Artin groups"[URL]
- A. Casson, "Automorphisms of Surfaces after Nielsen and Thurston, LMS Student Texts 9" (1988), Cambridge University Press
- R. Charney, "An introduction to right-angled Artin groups", Geom. Dedicata, 125, pp.141~158 (2007)
- J. Crisp, "Surface subgroups of right-angled Artin groups", Internat. J. Algebra Comput, 18(3), pp.441~491 (2008)
- J. Crisp, "Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups", Algebr. Geom. Topol, 4, pp.439~472 (2004)
- C. Droms, "Isomorphisms of graph groups", Proc. Amer. Math. Soc, 100(3), pp.407~408 (1987)
- J. Gross, "Topological Graph Theory" (1987), John Wiley and Sons
- J. Kim, "Hyperbolic Surface Subgroups of Right-Angled Artin Groups and Coxeter Groups", 박사, pp.2011
- S. Kim, "Hyperbolic Surface Subgroups of Right-Angled Artin Groups and Graph Products of Groups", 박사, pp.2007
- S. Kim, "On right-angled Atrin groups without surface subgroups", Groups Geom. Dyn, 4(2), pp.275~307 (2010)
- R. C. Lyndon, "Combinatorial Group Theory" (1977), Springer
- H. Servatius, "Surface subgroups of graph group", Proc. Amer. Math. Soc, 106(3), pp.573~578 (1989)