The topology of graph products of groups

John Meier
1994 Proceedings of the Edinburgh Mathematical Society  
Given a finite (connected) simplicial graph with groups assigned to the vertices, the graph product of the vertex groups is the free product modulo the relation that adjacent groups commute. The graph product of finitely presented infinite groups is both semistable at infinity and quasi-simply filtrated. Explicit bounds for the isoperimetric inequality and isodiametric inequality for graph products is given, based on isoperimetric and isodiametric inequalities for the vertex groups.
doi:10.1017/s001309150001899x fatcat:dedq7im4n5eircdt5fapj7jkqe