Minimality Conditions in Topological Groups

Abstract

This is a survey on the recent progress in minimal topological groups, with a particular emphasis on constructions leading to non-abelian minimal groups, as semidirect products, generalized Heisenberg groups and other groups naturally arising in Analysis and Geometry. A special attention is paid to several generalizations of minimality (as local minimality, relative minimality and co-minimality), the relations of minimality to (dis)connectedness and to various level of compactness and completeness.