Free products of topological groups with amalgamation

Abstract

The fundamental problem is to determine if the free product with amalgamation of Hausdorff topological groups exists and is Hausdorff. This is known to be true if the subgroup being amalgamated is central or if all groups concerned are kω and the amalgamation subgroup is compact. In this paper a general result is proved which allows one to move outside the class of compact or central amalgamations. Using this result it follows, for example, that the amalgamated free product F* AG exists and is Hausdorff if F, G and A are &ω-groups and A is the product of a central subgroup and a compact subgroup.