SOME RECENT RESULTS ON EXTENSIONS AND QUASI-HOMOMORPHISMS OF TOPOLOGICAL ABELIAN GROUPS : To the memory of Pawel Domanski (1959-2016) (Research Trends on Set-theoretic and Geometric Topology and their cooperation with various branches)

Abstract

The present paper is an enlarged version of a talk given at the RIMS Meeting on Set Theoretic and Geometric Topology held in Kyoto University from June 12 to June 14, 2017. Its goal, as well of that of the talk it grew from, is to give a motivation for the theory of extensions of topological abelian groups, including some recently published results. It has no pretenses at completeness, but on the way to presenting the main theorems we touch on several topics (as those of quasi-homomorphisms, cross sections or three-space problems) that arise naturally in connection with this subject.