The Tits alternative for non-spherical triangles of groups
Johannes Cuno and Jörg Lehnert
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Submission date: 14. May. 2014
published in: Transactions of the London Mathematical Society, 2 (2015) 1, p. 93-124
DOI number (of the published article): 10.1112/tlms/tlv005
MSC-Numbers: 20E06, 20F05, 20F65, 20E05, 20E07
Keywords and phrases: Tits alternative, triangles of groups, disc pictures, metric simplicial complexes, non-positive curvature
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Triangles of groups have been introduced by Gersten and Stallings. They are, roughly speaking, a generalisation of the amalgamated free product of two groups and occur in the framework of Corson diagrams. First, we prove an intersection theorem for Corson diagrams. Then, we focus on triangles of groups. It has been shown by Howie and Kopteva that the colimit of a hyperbolic triangle of groups contains a non-abelian free subgroup. We give two natural conditions, each of which ensures that the colimit of a non-spherical triangle of groups either contains a non-abelian free subgroup or is virtually solvable.