Fundamental groups of graphs of groups satisfy the finitely generated intersection property precisely when vertex groups, edge double cosets, and graph structure meet stated conditions, with an explicit decidable criterion for graphs of locally quasi-convex hyperbolic groups with virtually Z edge 2.
Sheaves on graphs, their homological invariants, and a proof of the Hanna Neumann conjecture: with an appendix by Warren Dicks
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The finitely generated intersection property in fundamental groups of graphs of groups
Fundamental groups of graphs of groups satisfy the finitely generated intersection property precisely when vertex groups, edge double cosets, and graph structure meet stated conditions, with an explicit decidable criterion for graphs of locally quasi-convex hyperbolic groups with virtually Z edge 2.