Topic Maps are the international industry standard for semantic information integration. Appropriate means for Topic Map exchange are crucial for its success as integration technology. Topic Map exchange bases on the governing Subject Equality decision approach, the decision whether two Subject Proxies indicate identical Subjects. This paper discusses the ‘absence of shared vocabularies’ in the context of these decisions. Thereby, a differentiation between Referential and Structuralist Subject Equality decision approaches is introduced. All existing approaches to Topic Map exchange base on the TMDM. This implies a Referential Subject Equality decision approach and bound to a concrete Subject Map Disclosure (SMD) ontology and Subject Map (SM) vocabulary. This paper introduces a Structuralist Subject Equality decision approach which is called SIM. It allows the exchange of Topic Maps in the absence of a shared SM ontology and SM vocabulary.