Manuscript Topics

At the International Congress of Mathematicians in Paris in 1900 David Hilbert stated 23 problems which influenced much of the research in mathematics of the 20^th century. His 5^th problem, in today’s terminology, asked whether every locally euclidean topological group accepted a compatible Lie group structure. It required half a century of effort on the part of several generations of eminent mathematicians until it was settled in the affirmative. Partial solutions came along as the structure of topological groups was understood better by Hermann Weyl and Fritz Peter who laid the foundations of the representation and structure theory of compact groups and a positive answer to Hilbert's Fifth Problem for compact groups was a consequence, drawn by John von Neumann in 1932. Lev Semyonovich Pontryagin Egbert Rudolf van Kampen developed in the 1930s the duality theory of locally compact abelian groups laying the foundations for an abstract harmonic analysis flourishing throughout the second half of the 20^th century and providing the central method for attacking the structure theory of compact abelian groups via duality and a positive response to Hilbert's question for locally euclidean abelian groups followed. Hilbert’s problem was finally solved in 1952 by Andrew Mattei Gleason and Dean Montgomery with important structure results by Kenkichi Iwasawa and Hidehiko Yamabe. With this major problem solved, there have been many advances in studying infinite-dimensional Lie groups, totally disconnected locally compact groups, etc. This Special Issue focuses on significant developments in topological group theory since the 20^th century.

Instructions for authors
https://www.aimspress.com/era/news/solo-detail/instructionsforauthors
Please submit your manuscript to online submission system
https://aimspress.jams.pub/